LAPPEENRANTA UNIVERSITY OF TECHNOLOGY
LUT School of Energy
Electrical Engineering
Eduard Ignatev
PERFORMANCE DEGRADATION MODELLING AND TECHNOECONOMIC ANALYSIS OF LITHIUM-ION BATTERY ENERGY
STORAGE SYSTEMS
First examiner Professor Jarmo Partanen
Second examiner Associate Professor Jukka Lassila
Supervisor Mikko Honkaniemi, ABB Power Grids, Vaasa
ABSTRACT
Lappeenranta University of Technology
LUT School of Energy
Electrical Engineering
Eduard Ignatev
Performance Degradation Modelling and Techno-Economic Analysis of Lithium-Ion
Battery Energy Storage Systems
Master’s thesis
2016
88 pages, 52 figures, 11 tables and 7 appendices
First examiner Professor Jarmo Partanen
Second examiner Associate Professor Jukka Lassila
Supervisor Mikko Honkaniemi, ABB Power Grids, Vaasa
Keywords: Lithium-ion, Lifetime, Battery energy storage system, Frequency Containment
Reserves, Net present value.
Transmission system operators and distribution system operators are experiencing new
challenges in terms of reliability, power quality, and cost efficiency. Although the potential of
energy storages to face those challenges is recognized, the economic implications are still
obscure, which introduce the risk into the business models.
This thesis aims to investigate the technical and economic value indicators of lithium-ion battery
energy storage systems (BESS) in grid-scale applications. In order to do that, a comprehensive
performance lithium-ion BESS model with degradation effects estimation is developed. The
model development process implies literature review on lifetime modelling, use, and
modification of previous study progress, building the additional system parts and integrating it
into a complete tool. The constructed model is capable of describing the dynamic behavior of
the BESS voltage, state of charge, temperature and capacity loss.
Five control strategies for BESS unit providing primary frequency regulation are implemented,
in addition to the model. The questions related to BESS dimensioning and the end of life (EoL)
criterion are addressed. Simulations are performed with one-month real frequency data acquired
from Fingrid. The lifetime and cost-benefit analysis of the simulation results allow to compare
and determine the preferable control strategy. Finally, the study performs the sensitivity analysis
of economic profitability with variable size, EoL and system price. The research reports that
BESS can be profitable in certain cases and presents the recommendations.
ACKNOWLEDGMENTS
This master’s thesis was carried out at the department of Electrical Engineering at Lappeenranta
University of Technology (LUT) School of Energy as part of the Double Degree program with
Moscow Power Engineering Institute (MPEI). I would like to thank all persons, who are
responsible for the existence of Double Degree program and making such an experience
possible.
I would like to give special thanks to my research supervisor Jukka Lassila, for his guidance
throughout the thesis and valuable comments, which helped to improve the work. I would also
like to thank my home university supervisor Alexander Polyakov for early stage discussions and
original suggestion to research the lithium-ion battery storages.
This work was also arranged with ABB Oy, Vaasa. I express my gratitude to Dmitry Vinokurov,
Mikko Honkaniemi, Seppo Pasto, and Julia Vauterin-Pyrhönen, who gave me this opportunity
to work on my thesis and get an inside look at Power Grids division in Vaasa.
Thanks to all my friends at Russia for sincere affection and missing me. I am also very grateful
for meeting a lot of pleasant people in Lappeenranta and making a connection with them.
Finally, I would like to acknowledge my family, especially my mother and father, for their
encouragement and enormous support over the years of my study. This thesis would not be
possible without them, and I infinitely appreciate it.
Eduard Ignatev
Lappeenranta, May 2016
TABLE OF CONTENTS
1. INTRODUCTION .................................................................................................................10
1.1. Research problem and objectives of the work ...............................................................12
1.2. Outline of the work ........................................................................................................12
2. OVERVIEW OF BESS TECHNOLOGIES AND THEIR APPLICATIONS ......................14
2.1. Comparison of battery technologies ..............................................................................14
2.2. Lithium-ion batteries ......................................................................................................15
2.2.1. Development of cell components and materials.....................................................17
2.2.2. Comparison of lithium-based chemistries ..............................................................20
2.3. Analysis and potential assessment of BESS applications ..............................................21
3. LITHIUM-ION BATTERY LIFETIME MODELLING .......................................................24
3.1. Lithium-ion battery aging mechanisms ..........................................................................24
3.1.1. Degradation due to cycling.....................................................................................27
3.1.2. Degradation due to storage .....................................................................................29
3.2. Lithium-ion battery lifetime models .............................................................................30
3.2.1. Cycling degradation models ...................................................................................31
3.2.2. Calendar degradation models .................................................................................38
3.3. Reviewed lifetime models summary ..............................................................................40
4. LITHIUM-ION BESS PERFORMANCE DEGRADATION MODEL ................................45
4.1. Battery circuit‐based model ...........................................................................................47
4.1.1. Specification of circuit elements ............................................................................50
4.1.2. General layout of equivalent circuit model ............................................................50
4.2. Lifetime model integration .............................................................................................51
4.3. BESS model ...................................................................................................................53
4.4. Simulation system overview ..........................................................................................55
5. PRIMARY FREQUENCY REGULATION PROVIDED BY BESS ...................................56
5.1. Finland ancillary service markets...................................................................................57
5.2. Simulation of BESS at FCR-N.......................................................................................59
5.2.1. Description of control logics ..................................................................................61
5.2.2. BESS dimensioning and the end of life criterion ...................................................68
5.3. Methodology ..................................................................................................................70
5.3.1. Lifetime estimation.................................................................................................70
5.3.2. Assessment of net present value .............................................................................71
5.4. Simulation results ...........................................................................................................73
5.4.1. Comparison of control logics .................................................................................73
5.4.2. Sensitivity analysis .................................................................................................76
6. CONCLUSION ......................................................................................................................81
6.1. Future work ....................................................................................................................82
REFERENCES ..........................................................................................................................83
APPENDIX I. BATTERY CELL TERMINOLOGY
APPENDIX II. LITHIUM-ION CELL USED IN MODEL DEVELOPMENT
APPENDIX III. CALENDAR DEGRADATION MODELS ADDITIONAL DATA
APPENDIX IV. MODEL INITIALIZATION FILE
APPENDIX V. DEGRADATION FUNCTIONS CONTENTS
APPENDIX VI. CONTROLLER SIMULINK BLOCK SET OF CONTROL LOGIC №5
APPENDIX VII. REPRESENTATIVE CASES NPV CALCULATION
6
LIST OF SYMBOLS
Ahth
Ampere-hour throughput [Ah]
b
Complex balancing factor
B
Pre-exponent factor
C0
Initial investment [EUR]
C1
Short time transient capacity [F]
C2
Long time transient capacity [F]
ce
Electricity price [EUR/MWh]
Ce
Loss due to efficiency [EUR]
Crate
Current rate
Ct
Cash flow [EUR]
DoD
Depth of discharge
Ea
Activation energy [kJ×mol-1]
EBESS
Total BESS capacity [MWh]
Icell
Cell throughput current [A]
ki
Kinetic dependence of the capacity fade evolution
Ncyc
Number of cycles
NPV
Net Present Value [EUR]
PFCR-N
FCR-N maximum bidding power [MW]
Prec charge
Charge power during recovery [p.u.]
Prec discharge Discharge power during recovery [p.u.]
Qcycling
Capacity loss due to cycling [%]
Qloss
Total capacity loss [%]
Qnom
Cell nominal capacity [Ah]
Qstorage
Capacity loss dues to storage [%]
r
Discount rate
r
Number of years for analysis
R
Universal gas constant [J×mol-1K-1]
7
R0
Cell internal resistance [Ohm]
R1
Short time transient resistance [Ohm]
R2
Long time transient resistance [Ohm]
R2
Long time transient resistance [Ohm]
SoC
State of charge
SoCmax
State of charge maximum limit
SoCmin
State of charge minimum limit
SoCref
State of charge set point
t
Number of cash flow year
t
Time
T
Temperature [K]
t15min
Full activation time period requirement [h]
Tref
Reference temperature [K]
Vcell
Cell terminal voltage [V]
VOC
Open-circuit voltage [V]
α 3-4
Constant fitting parameters
α
Parameter of the severity factor function
β
Parameter of the severity factor function
β 3-4
Constant fitting parameters
γ1 - 3
Constant fitting parameters
γ1 - 3
Constant fitting parameters
η
Battery efficiency [%] [Ohm]
λ
Transport properties of solvent molecule through SEI layer
8
LIST OF ABBREVIATIONS
BESS
Battery Energy Storage System
CAES
Compressed Air Energy Storage
CE
Continental Europe
DoD
Depth of Discharge
EIS
Electrochemical Impedance Spectroscopy
ENTSO-E European Network of Transmission System Operators for Electricity
ESS
Energy Storage System
FCR
Frequency Containment Reserves
FCR-D
Frequency Containment Reserve for Disturbances
FCR-N
Frequency Containment Reserve for Normal operation
FES
Flywheel Energy Storage
FRR
Frequency Restoration Reserves
LCO
Lithium Cobalt Oxide
LCP
Lithium Cobalt Phosphate
LFP
Lithium Iron Phosphate
LMO
Lithium Manganese Oxide
LMP
Lithium Manganese Phosphate
LNO
Lithium Nickel Oxide
LTO
Lithium Titanium Oxide
NC LFCR Network Code on Load-Frequency Control and Reserves
NCA
Nickel Cobalt Aluminum Oxide
NMC
Nickel Manganese Cobalt Oxide
NMO
Nickel Manganese Oxide
NPV
Net Present Value
OCV
Open-circuit Voltage
PHS
Pumped Hydroelectric Storage
RC
Resistor-Capacitor
9
RR
Replacement Reserves
SEI
Solid Electrolyte Interphase
SMES
Superconducting Magnetic Energy Storage
SoC
State of Charge
SoH
State of Health
TSO
Transmission System Operator
10
1 INTRODUCTION
A substantial amount of global electricity generation growth took place over the last decade.
The effect of population growth and progress in industrial technology is becoming a threat since
it clearly impacts the growing energy demands of a society which have to be satisfied. Main
sources of energy today are fossil fuels, nuclear energy, and renewable sources. Fossil fuels
contribute almost 70% of global electricity generation. Unfortunately, the complication with
fossil fuels is that their amount in the world is limited. Also, they produce a considerable amount
of CO2 emissions to the atmosphere. To limit the level of pollution by burning fossil fuels,
future electrical energy generation will have to develop a bigger reliance on renewable energy
sources, thus contributing to the environment improvement (Skea 2008, 8). High penetration of
variable generation such as solar and wind energy brings uncertainty and instability to the grid
due to their intermittent nature. The uncertainty creates challenges for system operators to
balance electricity generation and demand while instability can manifest itself in frequency
fluctuations. Energy Storage Systems (ESS) has been identified as one of the most rational
option to overcome those issues. ESS has always received a lot of attention from power systems
stakeholders as part of various applications to improve operating conditions and increase their
profits. A numerous amount of EES applications review papers are getting published on a
regular basis (Zidar et al. 2016, Luo et al. 2015, Medina et al. 2014) which indicates the
continuous progress, certain future prospects, and unresolved research questions.
The range of different ESS is very broad. There is no a particular best storage solution, and the
choice is always depending on requirements. Recent advances in battery technology have
induced keen interest in Battery Energy Storage Systems (BESS). A large body of data was
dedicated to the development of advanced cell component materials (Gulbinska (ed.) 2014;
Zhuang et al. 2014; Prosini 2011) and promising ways of BESS applications for system
operators, utility and customers services (Fitzgerald et al. 2015; Eyer and Corey 2010). For
many years, lead-acid and nickel-cadmium technologies have been the only viable options as a
secondary stationary battery until the early 1990s appearance of lithium-ion cell chemistry. By
11
this moment, Lithium-ion has undergone huge improvement development and considered to be
one of the leading battery technology candidate available. It is also expected that Lithium-ion
batteries will play a bigger role in the future formation of electric grid due to technical, economic
and policy advantageous aspects. A place of the lithium-ion batteries among other energy
storage technologies is demonstrated in Figure 1.1.
Lead-acid
Nickel-cadmium
Secondary batteries
Nickel-metal hydride
Hydrogen
Lithium-ion
Electrochemical
Sodium-sulfur
Zinc Bromine
Flow batteries
Vanadium Redox
Energy
Storage
Technologies
Supercapacitor
Electrical
Thermal
Superconducting
Magnetic Energy
Storage (SMES)
Pumped
Hydroelectric
Storage (PHS)
Mechanical
Compressed Air
Energy Storage
(CAES)
Flywheel Energy
Storage (FES)
Figure 1.1. ESS technologies hierarchy.
12
Battery system operators, developers, and decision makers must have access to reliable
information about the performance and lifetime of a lithium-ion battery, as well as optimal
operational strategies of BESS. A better understanding of aging mechanisms and cell behavior
modelling is an effective way to reduce life-cycle costs of BESS, which is the key aspect for the
feasibility of integrating it in ancillary services. For these reasons, comprehensive analysis of
different sources that have been investigating degradation effects caused by various factors with
respect to the cell chemistry is needed. Moreover, additional studies dedicated to techno–
economic analysis of battery storages have to be carried out due to changing power industry
regulations and cell price reduction. Based on that knowledge, certain recommendations for
decision making could be made such as selecting, sizing, location and operating conditions of
the BESS.
1.1 Research problem and objectives of the work
The main objectives of the research in this thesis are:
 Aggregate recently reported findings and provide an updated picture of the BESS
technology state of art;
 Investigate lithium-ion cell ageing phenomena and compare available degradation
models;
 Develop a practical lithium-ion BESS model with ability to describe dynamic
performance behavior and to estimate degradation effects;
 Design and conduct a series of simulations to analyse techno-economic feasibility of
BESS providing primary frequency regulation service;
1.2 Outline of the work
This thesis is structured as follows: Chapter 2 introduces a comparison of available battery
technologies with an in-depth view of lithium-ion chemistry and also presents the analysis of
promising BESS applications. Chapter 3 provides a literature review trying to cover the topic of
13
lithium-ion cell ageing mechanisms. Further, the reported lifetime models are compared, and
one of them is selected. Chapter 4 represent the development process of performance
degradation BESS model based on LFP chemistry. Chapter 5 addresses the feasibility of
frequency regulation service provided by BESS in Finland.
Background
research
Lifetime
modelling
investigation
Figure 1.1. Research process plan.
Performance
degradation
BESS model
Real data
simulations
Technoeconomic
analysis
14
2 OVERVIEW OF BESS TECHNOLOGIES AND THEIR APPLICATIONS
In this chapter, a range of electrochemical energy storage technologies is discussed. Main
technical characteristics of secondary batteries are compared. Lithium-based batteries selection
is justified, and further classification regarding component materials is carried out. It was done
in order to emphasize the contrast of batteries which belong to the same type.
2.1. Comparison of battery technologies
It goes without saying that main component of battery storage is an electrochemical cell. For
several decades’ batteries have been one of the most common direct current sources for many
industrial applications and power utilities. A term battery refers to the range of secondary
electrochemical cells connected in series and parallel. Cell produce electricity as a result of the
electrochemical reaction. Constant efforts are being made to advance the battery performance
characteristics, prolong their lifetime and decrease manufacturing costs. The most commonly
used battery cell technologies comparison is presented in Table 2.1.
Table 2.1. Technical comparison of battery storage technologies (Luo et al. 2015, Mahlia et al. 2014).
Technology
Development
Energy
density
(Wh/kg)
Cycle
efficiency
(%)
Lifetime (full
equivalent cycles)
Capital cost
(€/kWh)
Lead-acid
Mature
20-35
60-90
200-2000
50-400
40-120
60-83
500-2500
800-2400
60-80
66
3000
300
90-100
1000-6000
450-3800
Nickel-cadmium Commercialized
Nickel-metal
hydride
Commercialized
Lithium-ion
Commercialized 100-200
Sodium-sulfur
Developing
150-240
>86
2000
280
Zinc-Bromine
Flow
Developing
37
75
>2000
900
Vanadium Flow
Developing
25
85
“unlimited number
of cycles”
< 20 years
1280
Special
features
Low cost,
poor
characteristics
"Memory
effect", toxic
Poor
efficiency and
limited
application
High cost
High
temperature
operating
Low energy
density
Low energy
density
15
From Figure 2.1, it can be seen that lithium-ion batteries outperform other battery technologies
in terms of ability to combine high gravimetric energy and power density. Most of the time
density characteristics are not so valuable for stationary batteries, unlike for portable
applications. However, in certain cases high specific power and energy values of the battery
could result in considerable savings from reduced footprint of the system, if for instance the
price of land is very expensive. Next section provides a more detailed analysis of Lithium-ion
cell subtypes and their state-of-art.
Figure 2.1. Ragone chart for various cell type (Advancing technology for America’s transportation future
2013, 14).
2.2. Lithium-ion batteries
Lithium battery cells is a collective term for cells that are composed of lithium metal or lithium
compounds. A lithium‐ion battery cell consists of two electrodes, cathode and anode, a separator
in between, and current collectors on each side of the electrodes. Figure 2.2 shows a schematic
representation of lithium-ion battery cell.
16
Figure 2.2. A schematic representation of a lithium‐ion battery cell (Fang et al. 2010).
Lithium-ion cells have common advantages such as a unmatchable combination of high energy
and power density, high coulombic efficiency, low self-discharge rate, no memory effect,
comparatively long lifetime, high charge and discharge current possibility and relatively mature
state-of-art.
On the other hand, lithium cells still represent a relatively high cost, certain modifications and
chemistries have safety issues, and the SoC estimation can be more complicated than in other
types of electrochemical cells.
The current research related to lithium batteries mostly focused on improving battery
characteristics by developing advanced electrode materials and electrolyte solutions, as well as
enhancing safety and reducing manufacturing costs. Next subsections are providing an overview
and comparison of lithium-ion materials without entering into deep chemical details, but rather
with a focus on operational characteristics differences.
17
2.2.1. Development of cell components and materials
The choice of components and materials greatly affects the performance and cost of a lithiumion cell, for example, it mainly defines the energy density, average cell potential and obviously,
different materials costs are not the same. The four major components of the lithium-ion battery
are the cathode, anode, electrolyte, and separator.
Cathode materials currently in use or under development are described in accordance with the
following three morphologies:
 Layered Rock Salt Structure Materials (two-dimensional)
 Spinel Structure Materials (three-dimensional)
 Olivine Structure Materials (one dimensional)
The first practical lithium-ion battery was developed by Goodenough et al. (1980) and it was
based on lithium cobalt oxide (LCO) LiCoO2 cathode material. LCO represents the twodimensional group. Although LCO demonstrates good performance characteristics, the main
drawbacks are high cost, low thermal stability, and fast capacity fade. Lithium nickel oxide
(LNO) LiNiO2 has a crystal structure with LCO, it has relatively high energy density and lower
cost than cobalt, but poor cycle life and even worse thermal stability. Lithium manganese oxide
(LMO) LiMnO2 is another material from the same group, it is also much cheaper and less toxic
compared to cobalt or nickel. However, the cycling performance of LMO is not satisfactory too.
Despite the fact that LiNiO2 and LiMnO2 turned out to be unsuitable in their simple form, the
formulation of advanced materials such as LiNi0.8Co0.15Al0.05O2 (NCA), LiNi0.5Mn0.5O2 (NMO)
and LiNi0.33Co0.33Mn0.33O2 (NMC) introduced considerable performance improvements. (Nitta
et al. 2015)
The three-dimensional spinel structure enables lithium ions to diffuse in all three dimensions,
thus benefiting in terms of lower cost and high stability, but reducing discharge capacity. The
most known compounds in this group are Li2Mn2O4 (LMO) and Li2Co2O4 (LCO).
18
A new class of compounds was developed by Padhi et al. (1997) which restricts lithium ions
diffusion to a single linear dimension. The limited ion mobility was minimized through the
development of nanoparticles and other techniques. Thus, modern representative material
LiFePO4 (LFP) presents relatively low energy density and average voltage, compared to other
lithium-ion chemistries, while surpassing them in thermal stability, lifetime and cost. Other
novel olivines such as LiMnPO4 (LMP) and LiCoPO4 (LCP) that provide 4.1 V and 4.8 V,
respectively are therefore gaining attention but have not reached market yet.
Cathode material mainly determines the discharge profile of the lithium-ion battery. Typical
profiles for three types of cathode structures are presented in Figure 2.3.
Figure
2.3.
Discharge
profiles
of
different
lithium‐ion
cathode
structures
(Brodd
ed.
2013,
Chapter 2, 10).
Natural graphite is the most inexpensive graphite material available, but its high reactivity to
electrolyte prevents its use as anode without modification. Technology to coat the graphite
surface with thin carbon layer has become widely used, enabling modified natural graphite to
replace mesophase graphite as the leading anode material.
19
As there is little scope to increase the capacity of graphite anode further, research has turned to
other new materials including metal oxides and alloying materials. For example, lithium
titanium oxide (LTO) compound Li4Ti5O12 provides a combination of excellent thermal
stability, high rate capability, rather high volumetric capacity and also long cycle life.
Unfortunately, LTO has much higher cost because of Ti and reduces the cell voltage. Alloying
materials provide much higher capacity than graphite, but a serious drawback is the large
expansion and contraction of volume which occurs during the charge–discharge process.
Volume change can cause cracking of the material and loss of electrical contact. Thus, it is
common for alloying anodes to have short cycle life and fast increasing cell impedance.
The electrolyte in a lithium-ion battery is a mixture of organic solvents and an electrolyte salt
compound. The common solvents are a mixture of cyclic carbonate esters, such as ethylene
carbonate and propylene carbonate, and linear carbonate esters, such as dimethyl carbonate and
diethyl carbonate. The solution is completed with the addition of a salt compound such as LiPF6
or LiBF4. Electrolyte solutions must enable the Li ions to transport freely, which requires both
high dielectric constant and low viscosity. For electrolyte salt, both LiPF6 and LiBF4 were
widely used, but LiPF6 has come to dominate the market as shown in Figure 2.4.
Figure 2.4. Lithium-ion battery electrolyte salt market (Yoshino 2014)
Research on the electrolyte solution is generally focused on one of three areas: functional
electrolyte additives, flame-resistant or nonflammable electrolyte solutions, and new electrolyte
20
salts. For instance, flame-resistance is usually provided by employing phosphate compounds in
some way, and salt like lithium bis(oxalate) borate, in particular, is considered to be very
promising due to low-cost.
All commercial separators so far have been made of polyolefins, but they provide only limited
heat resistance. New separators are expected to offer not only high temperature stability and
safety but also improved ion transportation for better rate capability at high current discharge.
2.2.2. Comparison of lithium-based chemistries
Relative comparison of the most promising lithium-ion chemistries is shown in Figure 2.5, and
a more detailed list can be found in Table 2.2.
Specific
energy
Specific
energy
Specific
energy
Specific
Power Cost
Cost
Life span
Safety
NCA
Life span
Specific
Power
Life span
Safety
LTO
Life span
Safety
NMC
Specific
energy
Cost
Specific
Power
Specific Cost
Power
Safety
LMO
Specific
energy
Specific
Power
Cost
Life span
Safety
LFP
Figure 2.5. Comparison of the most promising lithium-ion battery chemistries (Dinger et al. 2010, De-Leon 2010).
21
Table 2.2. Technical comparison of lithium-ion battery chemistries (De-Leon 2010, Nitta et al. 2015).
Cathode
Lithium Cobalt Oxide
(LCO)
Nickel Cobalt Aluminum
Oxide (NCA)
Lithium Iron Phosphate
(LFP)
Lithium Manganese Oxide
(LMO)
Lithium Manganese Oxide
Spinel (LMO)
Lithium Manganese Oxide
Spinel Polymer (LMO)
Nickel Manganese Cobalt
Oxide (NMC)
Lithium Manganese Oxide
Spinel (LMO)
Lithium Nickel Oxide
(LNO)
Lithium Manganese
Nickel Oxide Spinel
(LMNS)
Lithium Manganese
Nickel Oxide Spinel
(LMNS)
Anode
Average
voltage,
V
Average
energy
density
Average
power
density
Lifetime
Safety
Cost
Graphite
3.7
High
Fair
Fair
Fair
High
Graphite
3.7
High
High
Fair
Fair
High
Graphite
3.3
Low
High
High
Graphite
3.8
High
High
Fair
Graphite
3.8
High
High
Fair
Good
Low
Graphite
3.8
High
High
Fair
Good
Low
Graphite
3.7
High
Fair
Low
Fair
High
Lithium Titanate
Oxide (LTO)
2.5
Low
Low
High
Good
High
Graphite
3.8
High
Fair
Fair
Fair
Fair
Graphite
4.8
High
High
Fair
Fair
Low
Lithium Titanate
Oxide (LTO)
3.2
Fair
High
High
Good
Low
Very
good
Very
good
Fair
Fair
To select a particular chemistry for further study, the specific priorities of battery characteristics
for particular BESS application must be defined.
2.3. Analysis and potential assessment of BESS applications
Many studies have been conducted investigating the possible value that BESS can provide to
the energy system over the past years. Some services and their definitions vary across all reports.
To demonstrate the value, services were categorized according to the stakeholder group that
receives the biggest part of benefits from each service. The stakeholder groups were identified
as supply, grid, and end-users. The supply group represents various energy generators, as well
as ancillary services requires by Transmission System Operators (TSO) to maintain a constant
22
balance between electricity supply and demand. The grid includes transmission and distribution
networks. End-users are located behind the meter where BESS can provide them a direct benefit.
The separation between stakeholder groups are rather vague, and should not be considered as
precise. Table 2.3 presents possible benefit values and basic technical characteristics of BESS
applications.
Table 2.3. BESS service values and key characteristics for particular applications (Fitzgerald et al. 2015; Lazard
2015; Eyer and Corey 2010; Technology Roadmap: Energy storage 2014)
Stakeholder
group
Supply
Grid
End-user
Service
Possible size,
MW
Estimated
response time
Service value,
$/kW-year
Spin / non-spin reserves
1 to 500
< 15 min
0 to 70
Load following
0.1 to 500
< 15 min
60 to 150
Energy arbitrage
1 to 500
hours
0 to 100
Black start
0.1 to 10
< 1 hour
10
Frequency regulation
0.1 to 10
seconds/minutes
10 to 200
Congestion relief
1 to 100
hours
10
Investments deferral
1 to 100
hours
50 to 150
Voltage support
1 to 10
seconds
50
Renewables integration
0.01 to 10
< 15 min
10
Time-of-use energy cost
management
0.01 to 1
hours
200
Demand charge reduction
0.01 to 1
< 15 min
20 to 200
Backup power
0.01 to 1
minutes
180 to 300
It has to be emphasized that values presented above are a very rough estimation and should not
be treated as an authoritative framework for resource planning or decision-making. This
considerable values uncertainty results from a great number of variables such as electricity
markets conditions, regulatory directions, and technical constraints.
Many studies highlighted the frequency regulation service as one of the most high-valued
application for BESS (Oudalov et al. 2007; Walawalkar et al. 2007). Moreover, Lazard’s
23
Levelized Cost of Storage Analysis (2015) claims that BESS based on lithium-ion technology
are already cost-competitive with their conventional alternative (gas turbine peaker). Frequency
regulation is characterized by short duration, but highly frequent BESS operation profile
throughout the lifetime. Specific power and energy density are not so critical for that application.
Consequently, the most important factors are a lifetime, safety and costs. In that case, the most
appropriate lithium-ion chemistry appears to be LFP and graphite anode. As a matter of fact, the
battery market researches by Bernhart and Kruger (2012) and by Pillot (2015) predict lithiumion cathode materials market grow double from 2015 through 2020 and triple through 2025,
while LFP is considerably increasing the overall share. The mentioned researches results are
shown in Figure 2.6.
a)
b)
Figure 2.6. Cathode market size forecast a) Bernhart and Kruger (2012); b) Pillot (2015).
Accordingly, next chapters of the thesis will present a development of BESS model based on
LFP cells and techno-economic evaluation of frequency regulation service in Finland.
24
3 LIFETIME MODELING OF LITHIUM-ION CELL
Lifetime modeling plays the critical role when the optimal type and optimal operation of BESS
are planned. At first in this chapter, a literature review of lithium-ion battery aging mechanisms
and stress factors will be conducted. Then some relevant capacity fading models will undergo a
comparison and finally a brief summary with final model selection will conclude the chapter.
Battery cell has many terms and definitions which describe its state and parameters. So in order
to clear the ambiguity and to avoid possible misinterpretation, the important cell terms used in
this thesis are explained in Appendix I.
3.1 Lithium-ion battery aging mechanismsEquation Chapter 3 Section 1
Understanding the details of lithium-ion batteries operation is not an easy task and
comprehension of aging mechanisms is even more complicated (Vetter et al. 2005, 1). The
problem is that factors contributing to aging process are not independent but rather have a
synergetic effect and occur at similar timescale. That creates a great effort for researchers who
tried to explore above mentioned phenomena throughout the years (Cheng Lin 2015, 1).
Since in this thesis LFP cathode and graphite anode are materials that were chosen as the
primary, following findings are related only to mentioned chemistry. For example, studies by
Li et al. (2016), Schlasza et al. (2014) and Liu et al. (2010) were focused to the particularity of
lithium iron phosphate electrode aging.
The results of battery degradation process include a decrease in remaining capacity (i.e. capacity
fade) and internal resistance rise. The aging mechanisms of cathode, anode, electrolyte and
separator differ significantly and therefore presented separately. Table 3.1 provides a summary
of aging mechanisms according to cell components, conditions that are enhancing the process
and the possible measures that reduce the effects.
25
Table 3.1. Aging mechanisms in LFP/graphite cells according to cell components (Lin et al. 2015; Schlasza et al.
2014; Vetter et al. 2005).
Cell
Failure subgroup
component
Current collector
corrosion
Aging mechanism
Result
Reduced by
Enhanced
by
Corrosion of Al in
combination with LiPF6
Impedance rise
Overpotential
Current
collector pretreatment
Low SoC
Change in surface porosity
Control charge
Crystal distortion
Capacity fading
Overcharge
cutoff voltage
Mechanical stress
Proper binder
High temp
Cathode Decomposition of
Binder dissolution
Capacity fading
binder
choice
High SoC
Dissolution of
Precipitation of new phases Capacity fading Temperature
High temp
soluble species
Loss of active material
Impedance rise
control
Delithiation of
Reaction of cell materials
High
Moisture intrusion
the surface
Climate control
with water
moisture
layer
Change in volume, surface
Overcharge
Morphological
Charge control
peeling of graphite,
Capacity fading
(very high
changes
cutoff voltage
cracking
SoC)
Lithium deposits and
Low temp
Capacity fading Temperature
Lithium plating
growth of dendrites (loss of
High C-rate
Impedance rise
control
lithium)
Bad design
Anode
Consumption of lithium
Stable SEIHigh C-rate
Capacity fading
SEI-layer* growth Resistive behavior becomes
layer*
High SoC
Impedance rise
more pronounced
(additives)
High DoD
Stable SEISEI-layer*
Decomposition due to high
Impedance rise
layer*
High temp
decomposition
temperatures
(additives)
Impurities
Electrolyte
Stability of electrolyte and Capacity fading
Alternative
High temp
decomposition
conduction salt
Impedance rise conductive salts
High SoC
Electrolyte
Reaction of conduction salt
Decrease in
High
Moisture intrusion
with water, hydrogen
Climate control
performance
moisture
fluoride formation
Separator
Separator properties and
Separator
destruction
failure modes
Morphological
changes
* Solid Electrolyte Interphase (SEI) – a passivating protective layer on anode
To have better insight on described processes they are demonstrated in Figure 3.1.
26
Figure 3.1. Representation of lithium-ion battery aging mechanisms (Schlasza et al. 2014).
Most of the researchers share the opinion that loss of active lithium ions due to their
immobilization in the SEI layer is the dominating mechanism responsible to capacity fade. Also,
the presence of iron particles inside SEI layer was noted at higher temperatures leading to a
reduction in graphite electrode accessibility (Li et al. 2016, 9). It can be concluded that the
capacity fading mainly occurs on the electrode/electrolyte interface due to its instability.
Liu et al. (2016) reported that LFP/graphite cells do not experience substantial internal
resistance increase after analyzing ageing experimental data. Since today’s power electronic
devices provide output in BESS and it capable to easily tune output power, this work will neglect
the impedance change due to degradation, with more focus on the capacity fade.
It is of great importance for lifetime modelling to figure out how the battery is operating or
environment conditions influence the ageing process. In general, lithium-ion cell degradation
can be divided into calendar aging and cycle aging.
27
3.1.1 Degradation due to cycling
After an explanation of ageing mechanisms, it is obvious that capacity fading will occur even if
the cell will be operated in ideal conditions due to natural wear off. Normal degradation trend
of lithium iron phosphate battery due to cycling can be seen in Figure 3.2.
Number of cycles
Figure 3.2. An example of capacity is fading due to the cycling of lithium iron phosphate battery.
In real-life applications, cells are not operated in ideal conditions and therefore experience
accelerated degradation under several stress factors. These stress factors are widely known from
the literature, and their effect will be described below respectively.
Temperature
Just like any other batteries, lithium-ion cells have their optimal temperature operation range.
Manufacturers tend to provide very wide range, like for example from -30 °C to +55 °C,
however, operating in the margin areas will not only lead to decreased performance but even
cause an accelerated degradation. Almost every cycling ageing study provides a pronounced
28
temperature effect on capacity fading similar to Figure 3.3. It is also worth noting that low
temperatures will significantly affect cell capacity too. It will happen by means of another
ageing mechanism known as lithium plating resulting rapid capacity fade, mostly during
charging.
Figure 3.3. Cell lifetime related to operating temperature.
Current rate (C-rate)
Cycling the battery with high currents rates will cause increased power dissipation by ohmic
heating on internal resistance. Consequently, that will generate heat and increased temperature
leading to high temperature degradation mechanisms described above. Significant voltage drop
on resistance can also result in overpotential. Except for that, high currents will also cause extra
mechanical stress on the electrodes invoking several ageing mechanisms.
State of charge (SoC)
The high level of SoC means anode of the cell is full of lithium ions and possess a high amount
of energy. SEI layer will grow faster in that state. Also, some other ageing mechanisms listed in
Table 3.1 will take place. The influence of high SoC is more profound during long storage time,
29
but the amount of time spent at certain SoC during cycling can play a role in ageing too.
Consequently, an impact from high SoC can be mitigated by cycling at lower SoC level, keeping
in mind that too low SoC will lead to current collector corrosion.
Obviously, the cell must be operated within SoC range recommended by the manufacturer, and
no overcharge or overdischarge should take place. Violation of these limits could lead to severe
damage to the cell. The battery management system (BMS) carrying out the operating limits
protective functions, i.e. it monitors the SoC, voltage and temperature and in the case of
thresholds violation, it can send an alarm message or even shut off the battery. BMS is also
responsible for SoC leveling among the cells in the battery pack.
Depth of discharge (DoD)
Many authors and manufacturers present the cycle life of the battery as a function of a number
of cycles, but do not specify the details about DoD of that cycling. In the case of evaluating a
possible number of cycles until the end of life (EoL), the larger the DoD, the more intercalation,
and deintercalation will take place due to natural wear-off leading to loss of lithium and active
material (Vetter 2012, 273). Because of that, less full cycles before the EoL are possible than a
number of cycles with minor DoD. Figure 3.4 shows an example of expected number of cycles
until the end of battery life with different DoD cycling. When the battery is operated with high
DoD, it undergoes low and high SoC states which effects were described above.
3.1.2 Degradation due to storage
Lithium-ion cells do not only degrade as a result of utilization. While on rest, SEI layer is
exposed to the electrolyte which can slowly enhance its growth. Thermodynamical stability of
the components and chemical side reactions inside the cell determine the ageing rate on storage.
Under the right conditions, capacity fade can be minimized, but in the case of exposure to
elevated temperatures, the activation energy of chemical reactions becomes lower and ageing
side reactions occur faster. High SoC is also increasing the reactivity and thus accelerating the
capacity fade as mentioned in the previous subsection.
30
Figure 3.4. An example of expected cycle lifetime as a function of DoD (Sauer 2012, 147).
3.2 Lithium-ion battery lifetime models
There are many approaches for lifetime modeling of lithium-ion batteries exist. Their
classification is shown in Figure 3.5. The first approach is usually referred as a post-processing
or offline and it is used for assessing the impact of a certain operating scheme on the expected
lifetime of the battery. It can be further divided into the counting of the amount of charge through
the battery (usually in Ah units or Wh in some cases) and cycles counting method. Both of these
methods can only handle the prepared output data, for example from the real system. The second
group of methods is called performance degradation models, and they represent the combination
of a lifetime model with the performance model. That solution gives the ability to perform on
stream calculations and make updates of the performance parameters depending on the
degradation rates. There are two major methods exists to estimate the battery performance: the
first method represents the equivalent circuit-based models, the second one uses physical
equations to describe the chemical kinetics and structural changes of components inside the
battery.
31
Figure 3.5. Classification of lifetime models.
The goal of this section is to perform a survey of most relevant pure lifetime practical models
available to the public, figure out their advantages along with drawbacks and finally compare
the outcomes of investigated models with each other. To minimize the divergence in results due
to specific chemistries characteristics and discrepancy of cells design, works that were focused
on typical cylindrical LFP/graphite cell had been chosen for analysis. The manufacturer
datasheet of the cell can be found in Appendix II. This particular cell was selected due to its
wide use and sufficient amount of reports among the scientific community. The models which
provided full description and characterization with numerical values of coefficients were
considered a priority because the end target was to use one of them in the following chapters.
3.2.1 Cycling degradation models
One of the most cited semi-empirical degradation models for LFP cells cycle life is proposed
by Wang et al. (2011). The result of the work was the establishment of a mathematical
relationship between capacity fade and temperature, C-rate and Ah-throughput.
32
The model provides a simple Equation 3.1 with variation of pre-exponent factor depending on
the C-rate (Table 3.2):
0.55
 31700  370.3  Crate 
Qcycling  B  exp 
   Ahth 
R T


(3.1)
Qcycling  capacity loss due to cycling [%]
B
 pre-exponent factor
Crate
 current rate
R
 universal gas constant 8.314 J/molK
T
 temperature [K]
Ahth
 ampere-hour throughput [A  h]
Table 3.2. Pre-exponent factor dependence on C-rate.
C-rate
B value
C/2
31,630
2C
21,681
6C
12,934
10C
15,512
The main advantage of this model is its simplicity, but it lacks the ability to consider complex
cycling profile and SoC influence is neglected. The correlation with experimental data is fair
enough, but during the model check, the contradictory question arises. It seems that at the same
temperature model results with more damage for C/2-cycling than 2C and 6C, but it has to be
the opposite way. Even if temperature correction within the cell due to additional heat been
made, the results does not change much (Figure 3.6). This basically means there is no clear
relation between current value and degradation rate, except for very high current zone where
degradation mechanisms such as lithium plating and rapid SEI-layer growth come into action.
33
C/2
2C
6C
60
10C
C/2
50
50
40
40
Capacity fade, %
Capacity fade, %
60
30
20
10
2C
6C
10C
30
20
10
0
0
0
10000
20000
30000
0
Ah-throughput
10000
20000
30000
Ah-throughput
Figure 3.6. Wang et al. (2011) model simulation results for 20ºC a) without temperature correction, b) with
temperature correction.
Suri and Onori (2016) modified the previous model, made recalibration and introduced linear
dependence on average SoC by values α and β from Table 3.3 instead of pre-exponent factor:
0.57
 31500  152.5  Crate 
Qcycling    SoC     exp 
   Ahth 
R T


SoC
 state of charge


 parameter of the severity factor function
 parameter of the severity factor function
Table 3.3. Values of severity factor function parameters α and β.
SoC [%] < 45
SoC [%] ≥ 45
α
2896.6
2694.5
β
7411.2
6022.2
(3.2)
34
Model simulation results on Figure 3.7a clearly show improvement in C-rated dependency. That
model should provide better results for applications with pronounced average SoC. It can be
noted that values of α and β are greater for < 45% SoC than for ≥ 45% SoC, thus leading to
higher degradation rate near the 45% SoC demonstrated on Figure 3.7b. Probably, this is the
result of a very few profiles data.
C/2
2C
6C
16
10C
14
14
12
12
Capacity fade, %
Capacity fade, %
16
10
8
6
2C
6C
10C
10
8
6
4
4
2
2
0
C/2
0
0
10000
20000
Ah-throughput
30000
0
10000
20000
30000
Ah-throughput
Figure 3.7. Suri and Onori (2016) model simulation results for 20ºC a) 50% SoC, b) 40% SoC.
Yuksel and Michalek (2012) on the other hand simplified the model by Wang et al. (2011) even
more. They disposed the C-rate consideration and obtained Equation 3.3 by using a least-squares
fit:
 4.257 10 4 
0.55
Qcycling  1.1443 10 6  exp 
   Ahth 
R T


(3.3)
Papers by Sarasketa-Zabala et al. (2015, 2016) provide a similar model, but with a focus on
DoD swing. He reported that C-rate effect was minimal or had inexplicable trends at certain
35
DoD levels, for that reason it was neglected. Equations 3.4 and 3.5 compose the overall
mathematical model for two ranges of DoD. Unfortunately, he does not provide fitting
coefficients, but his experimental results in Figure 3.8 can serve as a reference. The DoD
influence presented in this study does not resemble any other models.
Qcycling   1  DoD 2   2  DoD   3   b  Ah0.87
10%  DoD  50%
1 - 3
 constant fitting parameters
DoD
 depth of discharge
b
 complex balancing factor that is a function of Ahth
Qcycling    3  exp  3  DoD    4  exp  4  DoD    k  Ah 0.65  DoD  10%;  50%
3 - 4
3 - 4
(3.4)
(3.5)
 constant fitting parameters
 constant fitting parameters
Figure 3.8. Sarasketa-Zabala et al. (2015) experimental and model fitting results for cycling at 1C, 50% middle
SoC and 30 °C.
Swierczynski et al. (2015a) investigated lifetime of BESS for integration with a wind turbine.
Therefore, an assumption was made that the idling of SoC should be 50% in order to provide
power both balancing up and down. Consequently, the SoC factor was neglected in his work.
36
Moreover, all ageing tests were performed with 4C charge and discharge current to consider
worst case scenario and speed up testing phase. Aside from that, temperature and cycle depth
were studied. Capacity fade in percent can be calculated with a single function:
Qcycling   3.0806 105  exp  0.03216  T     0.9049  exp  0.00972  DoD    N cyc 0.5
N cyc
 number of cycles
DoD
 depth of discharge [%]
(3.6)
Model simulations on Figure 3.9 were performed for several DoD levels, and results were
converted in Ah-throughput dependency to compare it with previous models.
30
30
20% DoD
60% DoD
20% DoD
100% DoD
100% DoD
25
25
20
20
Capacity fade, %
Capacity fade, %
60% DoD
15
10
5
15
10
5
0
0
0
5000
10000
Number of cycles
15000
0
10000
20000
30000
Ah-throughput
Figure 3.9. Swierczynski et al. (2015a) model simulation results for 20ºC a) number of cycles dependency,
b) Ah-throughput dependency.
The same year later Swierczynski et al. (2015b) carried out another paper about lifetime
modelling but for electric vehicles application. While all the cycling test cases remained the
37
same (50% SOC and 4C-rate), the term for DoD consideration and other fitting parameters have
changed. Capacity loss due to cycling in updated model can be calculated by Equation 3.7;
results were treated the same way to show Ah-dependency and presented on Figure 3.10:
Qcycling  0.00024  exp  0.02717  T   0.02982  DoD 0.4904  N cyc 0.5
 depth of discharge [%]
DoD
30
30
20% DoD
60% DoD
20% DoD
100% DoD
25
25
20
20
Capacity fade, %
Capacity fade, %
(3.7)
15
10
5
60% DoD
100% DoD
15
10
5
0
0
0
5000
10000
Number of cycles
15000
0
10000
20000
30000
Ah-throughput
Figure 3.10. Swierczynski et al. (2015b) model simulation results for 20ºC a) number of cycles dependency,
b) Ah-throughput dependency.
After conversion from a number of cycles to Ah-throughput value, it is clearly noticeable that
curves for different DoD are matching together. Indeed, the assumption that the terms DoD0.4904
and DoD0.5 can be equated will not contribute a huge error, especially with the fact that results
of various models differ significantly, and all estimations are very rough. That will allow to
express the function through Ah-throughput in Equations 3.8 – 3.10.
38
Ahth  2  N cyc  DoD  Qnom
(3.8)
Ahth
2  Qnom
(3.9)
DoD 0.5  N cyc 0.5 
Qcycling  0.00024  exp  0.02717  T   0.02982 
Qnom
Ahth
2  Qnom
(3.10)
 cell nominal capacity [Ah]
An interesting way for taking into account more specific cycling conditions was suggested by
Millner (2010) and extended by Xu (2013) later on. The model is based on theoretical models
of crack propagation in structural materials. The impact of each stress factor expressed in the
form of linearized degradation function and simply are multiplied by each other representing
total degradation rate of the certain cycle. To count and identify all the cycles, Rainflow cyclecounting algorithm is applied to complex SoC curve, giving out the amplitude (DoD), the mean
value (SoC average), begin and end moments of time. Using exact time moments, average
temperature and C-rate of each cycle are calculated. Unfortunately, the fitting parameters are
determined with experimental data for lithium manganese oxide (LMO) batteries and therefore
cannot be used for LFP.
3.2.2 Calendar degradation models
Along with the cycle-life model, Yuksel and Michalek (2012) described calendar ageing of the
same LFP/graphite cell with two equations obtained from manufacturer’s data:

Qstorage  (0.23  T  67)  log10(t )  (0.3  T  88.95), for T  45C


Qstorage  (0.23  T  67)  log10(t )  (0.013  T  2.36), for T  45C
Qstorage  capacity loss due to storage [%]
t
 storage time [days]
(3.11)
39
The technical data obtained from the manufacturer should always be treated with skepticism. In
any case, this model does not take into account the SoC at which battery is stored while this
factor plays a huge role in storage degradation.
Another successful model with the empirical expression for predicting capacity fade was made
by Grolleau et al. (2014). It considers both temperature and SoC influence in kinetic dependence
term k (T, SoC) and requires to solve differential Equation 3.12:
dQstorage
dt
 Qstorage (t ) 
 ki T , SoC   1 

Qnom 

  (T )
(3.12)
ki
 kinetic dependence of the capacity fade evolution with T and SoC during storage

 transport properties of solvent molecule through SEI layer
k (T , SoC )  A(T )  SoC  B(T )
(3.13)
 Ea  1
1
A(T )  k A  exp   A   
 R  T Tref



 


(3.14)
 Ea
B (T )  k B  exp   B
 R


 


(3.15)
Eai
 activation energy [kJ×mo -1 ]
Tref
 reference temerature 298 K
1
1
 
T T
ref

Estimated model parameters after non-linear regression of aging data are presented in Table 3.4.
Table 3.4. Estimated model parameters.
Parameter
λ
kA
EaA
kB
EaB
30ºC
3
Temperature
45ºC
3
4.39×10-5
182 kJ mo-1
1.01×10-3
52.1 kJ mo-1
60ºC
7
40
Besides the cycling degradation model mentioned above, Swierczynski et al. (2015a, 2015b)
provide a calendar ageing estimation. Since in the first work, it was considered that the idling
SoC of the BESS is equal to 50%, the lifetime of the battery cells in this model is only dependent
on the storage temperature and storage time. The final function takes form:
Qstorage  4.05 105  exp  0.035  T   t 0.5
T
 temperature [C ]
t
 storage time [months]
(3.16)
Second paper also takes into account SoC at which the battery is stored and have totally different
fitting function and parameters:
Qstorage   0.019  SoC 0.823  0.5195    3.258 109  T 5.087  0.295   t 0.8
SoC
 state of charge [%]
T
 temperature [C ]
t
 storage time [months]
(3.17)
For calendar degradation evaluation Xu (2013) applies the same approach with linearized
increment capacity loss multiplied by average temperature and SoC, but as mentioned before
the characterization was performed for another cell chemistry.
3.3 Reviewed lifetime models summary
Figure 3.11 and Figure 3.12 demonstrate the most similar cases and conditions for cycling and
calendar models respectfully with the addition of some experimental data and mean value curve.
The data from calendar models for temperatures other than 20°C can be found in Appendix III.
41
22
20
18
16
Capacity fade, %
14
12
10
8
6
4
2
0
0
5000
10000
15000
20000
25000
Ah-throughput
Mean value;
Wang et al. (2011): 0,5C-6C
Yuksel and Michalek (2012)
Suri and Onori (2016): 50% SoC, 0.5C;
Suri and Onori (2016): 50% SoC, 6C;
Swierczynski et al. (2015a): 50% SoC, 100% DoD, 4C;
Swierczynski et al. (2015b): 50% SoC, 100% DoD, 4C;
Sarasketa-Zabala et al. (2015) reconsctructed: 50% SoC, 100% DoD, 1C;
Figure 3.11. Cycling degradation data acquired from examined models and sources (T = 20÷25°C)
30000
42
6
Capacity fade, %
5
4
Yuckel and Michalek (2012)
Grolleau et al. (2014)
3
Sqierczynsky et al. (2015a)
Swierczynski et al. (2015b)
2
Li et al. (2016) reconstructed
Mean value;
1
0
0
100
200
300
t, days
400
500
600
Figure 3.12. Calendar degradation data acquired from examined models and sources (T=20°C, 50% SoC).
Analyzing the results of investigated LFP/graphite cell degradation models, the following
conclusions can be drawn:
 Despite the reviewing of models with the same lithium-ion chemistry, the estimations
are considerably divergent, which makes the generalization not possible;
 Cycling degradation curves look identical due to similar terms in equations, whereas
calendar functions are fundamentally different and do not follow a single trend;
 A variety of models creates difficulties for comparison of their performance since they
consider different set of stress factors and making specific assumptions;
 It was noted that almost in every set of conditions both in cycling and calendar, the
results from Swierczynsky et al. (2015b) happen to be closer to mean value than other
models, consequently it was decided to utilize it in the next chapter;
43
Selecting the cycling model by Swierczynsky et al. (2015b) comes with certain assumptions.
Authors of the work mentioned that the cycling test cases have been performed with a 4C rate,
but it is rarely the case in applications like frequency regulation. Consequently, the obtained
estimation of BESS lifetime can be too optimistic. However, many studies report that C-rate
stress factor can be neglected. For example, Marano et al. (2009) claim that C-rate range under
4C does not introduce to any significant effect unlike currents up to 10C or 15C. As mentioned
before, Sarasketa-Zabala et al. (2015) find the effect of C-rate is minimal for some of the tests
as shown in Figure 3.13. The capacity degradation trend for the test case with 60% DoD and 2C
is not in agreement with the general theory, which implies higher C-rate as a more severe stress
factor. On the contrary, the 3.5C cycling case did not demonstrate any signs of accelerated
degradation, but 2C degradation rate was definitely enhanced. The case in point could be a cell
malfunction or non-linear combined effects of DoD and C-rate, but since there were no
additional tests, it was decided to neglect this case and C-rate effect on cycling ageing.
Figure 3.13. C-rate effect on the capacity fade (Sarasketa-Zabala et al. 2015).
44
Authors also add that the effect of Ah-throughput overlaps the C-rate effect and considered more
significant. It was also emphasized previously in Wang et al. (2011) model simulation results
that only high C-rates like 10C have pronounced effect. The information described above gives
reason to believe that utilizing Swierczynsky et al. (2015b) with C-rates lower than 4C is
acceptable and will not cause misconception.
Finally, the important question is how to define overall capacity loss. Only a few works give
adequate explanations on how they took into account simultaneous cycling and calendar ageing
(i.e. isolating the “pure” cycling effect) on experimental stage (Schmalstieg et al. 2013, Fares
2015). Despite a mentioned uncertainty, the general trend among many researchers
(Guenther et al. 2013, Xu 2013, Yuksel and Michalek 2012, Sarasketa-Zabala et al. 2016,
Swierczynski et al. 2015b) is assuming that total capacity degradation can be determined by
simple sum up of cycling and calendar ageing values, therefore, the same principle will be
realized during model implementation.Equation Chapter 4 Section 1
45
4 LITHIUM-ION BESS PERFORMANCE DEGRADATION MODEL
The next logical step towards BESS techno-economical analysis is to develop a proper
functioning performance model that will be able to evaluate capacity degradation. In
Chapter 3, a practical LFP cell lifetime model has been proposed. In this chapter, the missing
parts of the BESS performance degradation model will be developed and integrated together.
As it was already mentioned in the previous chapter, the battery performance models serve
engineers as a tool to simulate battery dynamic behavior for particular applications and systems.
Two major types of these models were categorized earlier:
 Electrochemical models;
 Equivalent circuit‐based models;
Although electrochemical models endowed with advantages such as providing high accuracy
and comprehension of fundamental physical processes inside the cell, they burden high
mathematical complexity and computation power. Moreover, they require a good knowledge of
electrochemistry. Since this thesis is written from the perspective of an electrical engineer,
electrochemical models are out of this work scope.
The equivalent circuit‐based models use electric circuit physical analogs to describe system
characteristics of a battery cell. By choosing different combinations of voltage sources, resistors,
and capacitors, and characterizing their parameters, circuit-based models are able to describe
voltage and capacity behavior of the cell without significant computational complexity. A vast
number of circuit models have been developed in the literature, most of them can further be
classified into two main groups:
 Lumped-parameter equivalent circuit models;
 Impedance-based models;
46
A very recent article by Nejad et al. (2016) systematically reviews the lithium-ion battery
equivalent circuit models for real-time simulations in terms of their accuracy and demands. The
models under investigations include the Combined model, Rint model, two hysteresis models,
Randles' model, a modified Randles' model and two resistor-capacitor (RC) network models
with and without hysteresis included. The authors also compared the two-RC model with
impedance-based type. The impedance-based model allows a direct measurement of system ACresponse in any working point and presents a close relation of elements to physic-chemical
processes inside the battery. However, in order to properly build that type of model, it requires
special equipment for electrochemical impedance spectroscopy (EIS). Overall, the results of the
review by Nejad et al. (2016) suggested that the two-RC model structure is an optimum choice
for implementation of most battery energy storages and power management strategies. The
equivalent circuit two-RC model structure diagram is shown in Figure 4.1.
I cell
 cell throughput current [A]
Vcell
 cell terminal voltage [V]
R0
 cell internal resistance [Ohm]
R1
 short time transient resistance [Ohm]
C1
 short time transient capacity [F]
R2
 long time transient resistance [Ohm]
C2
 long time transient capacity [F]
VOC
 open-circuit voltage [V]
Figure 4.1. The equivalent circuit diagram for the two-RC model.
47
The self-discharge rate of lithium-ion cells is very low, which is approximately 1-3% per month
(Swierczynski et al. 2014, 1), consequently the parasitic branch will be neglected.
Next sections describe the development of lithium-ion BESS model including degradation
effects using Matlab®, Simulink™ and Simscape™ modeling environment.
4.1 Battery circuit‐based model
The publicly available equivalent circuit model of lithium battery cell with two-RC blocks
developed by Huria et al. (2012) was adopted and upgraded for the needs of this thesis. The
original model accounts for the dynamic behavior of the cell, including non-linear open-circuit
voltage (OCV), passive circuit elements state of charge and inner temperature. Elements of the
cell VOC, R0, R1, C1, R2, C2 are functions of SoC and temperature. A runtime operation of the
model is implemented through coulomb counting technic, i.e. integrating the current flow over
time as shown in Equation 4.1.
t
 I  t dt
cell
SoC  1 
0
Qnom
(4.1)
Numerical values of the model were estimated for high power NMC cells. Hence, new
characterization for LFP cell type is necessary.
4.1.1 Specification of circuit elements
Ding et al. (2012) executed parametrization of corresponding circuit elements for cylindrical
LFP/graphite cell. Applying their results will allow integrating performance model with
degradation model derived in the previous chapter for the same battery product. Current
direction dependency does not have a perceptible effect on results, so it was neglected to avoid
immensely high complexity. The circuit elements in models are described by lookup tables. The
parameters of passive circuit elements presented in Figure 4.2 and 4.3 were digitized in matrix
form with the help of GetData Graph Digitizer software and used in the model.
48
Figure 4.2. Transient passive elements values with dependence from temperature and SoC (Ding et al. 2012).
Figure 4.3. Inner resistance values with dependence from temperature and SoC (Ding et al. 2012).
The internal resistance R0 has a minimum dependence on SoC but is highly dependent on
temperature. The transient passive elements have both temperature and SoC dependency.
49
Figure 4.4. The measured charging and discharging OCV as a function of SoC (Weng et al. 2013).
The OCV relation with SoC in LFP cells is a topic for discussion among many researchers.
Indeed, LFP cells have very flat charge and discharge curve, so even a small mismatch may
cause a large deviation of two values. Some authors observed pronounced hysteresis effect of
the OCV during charging and discharging process (Omar et al. 2014, 1579), while others did
not.
Weng et al. (2013) proposed a new method of obtaining OCV by taking the average of charging
and discharging data, as shown in Figure 4.4. Also, the OCV curve from Weng et al. (2013)
paper is based on a lifecycle test data collected from cylindrical LFP cells. Owing to this,
Figure 4.4 was used to parametrize OCV look-up table as a function of SoC.
Nominal battery capacity and approximate thermal properties were acquired from manufacturer
datasheet presented in Appendix II. Overall summary of model parametrization is embodied
within Matlab initialization file and provided in Appendix IV.
50
4.1.2 General layout of equivalent circuit model
The core equivalent circuit elements were created using Simscape™ simulation tool, and
basically, they consist of block parameter estimation part using look-up tables and elementary
electrical circuit equations. It has to be noted that original model contained thermal modelling
feature based on power dissipation of circuit elements. Figure 4.5 shows the model block set
with explanations.
Equations
v = i · R0
R0 table look-up
R0 = f (T)
Capacity calculation
SoC calculation
Equations
v = i · R1
i = C1 · dv/dt
Equations
v = i · R2
i = C2 · dv/dt
OCV table look-up
VOC = f (SoC)
C1 table look-up
C1 = f (SoC, T)
C2 table look-up
C2 = f (SoC, T)
R1 table look-up
R1 = f (SoC, T)
R1 table look-up
R2 = f (SoC, T)
Figure 4.5. The Simscape™ layout of the 2RC battery cell model.
Power dissipation
P=i·v
Thermal subsystem
51
To check the dynamic performance of newly parametrized LFP equivalent circuit model, full
charge and discharge with 1C pulse current tests were conducted, and results are demonstrated
in Figure 4.6.
a)
b)
Figure 4.6. The voltage dynamic test of fully a) charging and b) discharging the cell.
52
4.2 Lifetime model integration
Incorporating degradation rate estimation in performance model of lithium iron phosphate
battery is one of the key aspects of present thesis. Based on results from Chapter 3, a model
developed by Swierczynsky et al. (2015b) was selected as the best candidate among other
options. Total capacity fade due to cycling and calendar simulated setting can be determined
from Equations 4.2 – 4.4.
Qloss  Qcycling  Qstorage
Qcycling  0.00024  exp  0.02717  T   0.02982 
(4.2)
Ahth
2  Qnom
Qstorage   0.019  SoC 0.823  0.5195    3.258 109  T 5.087  0.295   t 0.8
Qloss
(4.3)
(4.4)
 total capacity loss [%]
Capacity degradation can be taken into account based on Equation 3.2. The code of OCV custom
block (Em_table), where capacity table look-up takes place, can be modified to subtract the
capacity loss from nominal capacity as shown in Figure 4.7.
Figure 4.7. Developing dependency of remaining capacity from degradation model output.
53
Selected lifetime model requires input data such as total Ah-throughput, simulation time, the
nominal capacity of the cell and finally average values of temperature and SoC. Since the
equivalent circuit model can be highly dynamic, in order to decrease inaccuracy and provide
average values of temperature and SoC, continuous RMS value blocks were implemented on
continuous input signals. Figure 4.8 introduces lifetime model block set, in addition, the contents
of cycling and calendar degradation Matlab functions are available in Appendix V.
Figure 4.8. The Simulink™ LFP cell lifetime model block set.
4.3 BESS model
Equivalent circuit and lifetime models are developed according to one single cell while BESS
contains a large amount of single cells interconnected in series strings which are connected in
parallels with each other. Complex battery pack structures introduce additional complications
in battery modeling. The research questions of this work did not consider the BMS, power
converters or modeling the variation of cells characteristics within the battery pack. Hence, all
cells are assumed to be completely identical. In other words, voltage, current, and energy are
evenly distributed among the cells. That simplification allows to convert the inputs and outputs
54
of the cell to a BESS level by simple Equations 4.5 – 4.6. A development from cell to BESS
model is shown in Figure 4.9.
I cell 
I BESS
N par
(4.5)
Vcell 
VBESS
N str
(4.6)
I BESS
 BESS current [A]
N par
 conditional number of parallel strings
VBESS
 BESS voltage [V]
N str
 conditional number of cells in one string
Figure 4.9. The Simscape™ cell - BESS transition block set.
55
4.4 Simulation system overview
Linking together two-RC equivalent circuit-based model including thermal modeling with
previously developed lifetime model and upscaling it to high power BESS level form a complete
dynamic simulation system. The main view is presented in Figure 4.10.
Figure 4.10. Overview of the BESS simulation model.
Besides initialization file containing essential system parameters, the model requires an input
current load profile or special control block that will provide the signal. Chapter 5 is dedicated
to frequency regulation service; therefore, several control algorithms will be developed to
govern the BESS.
Equation Chapter 5 Section 1
56
5 PRIMARY FREQUENCY REGULATION PROVIDED BY BESS
In recent years’ ancillary service markets have been opened by some countries, such as Finland
and services like frequency regulation have become profit-making. BESS can be a very useful
tool for maintaining system frequency within the desired level. Power electronics inverters with
very fast response time within the BESS can provide much faster regulation than Pumped
Hydroelectric Storage or Gas Turbine. This is becoming more valuable considering growing
trend of time outside the band 49.90 – 50.10 Hz in Nordic countries (ENTSO-E 2011) and hour
shift imbalance problems (Barmsnes 2014). Indeed, the frequency histogram of March 2016
measured by Fingrid in Figure 5.1 indicates a big amount of incidents outside the dead-band.
Figure 5.1. Distribution of frequency values in Finland during March 2016.
In order to investigate the techno-economic feasibility of frequency regulation service in this
chapter, the concept from Figure 5.2 was employed.
Figure 5.2. The scheme of the BESS frequency regulation service assessment.
57
5.1 Finland ancillary service markets
In Finland, ancillary service markets are held by national transmission system operator Fingrid.
Ancillary services which represent frequency control processes are categorized as reserves. The
structure of power reserve markets in Fingrid is presented in Figure 5.3.
Figure 5.3. Reserve products used in Finland (Fingrid 2016).
Reserves are divided into Frequency Containment Reserves (FCR), Frequency Restoration
Reserves (FRR) and Replacement Reserves (RR). FCR are used for the constant control of
frequency. The purpose of FRR is secondary control and to relieve FCR units. RR release
activated FRR back to a state of readiness in case of new disturbances. FCR are subdivided in
Frequency Containment Reserve for Normal operation (FCR-N) and Frequency Containment
Reserve for Disturbances (FCR-D). The aim of FCR-N is to maintain the frequency in the
normal range of 49.9 – 50.1 Hz. The aim of FCR-D is to replace the production deficit in the
case of unexpected disconnection of generation or interconnector. The technical requirements
for above mentioned reserves are listed in Table 5.1. (Fingrid)
58
Table 5.1. The technical requirements for reserve products.
Reserve
Minimum
size
FCR-N
0.1 MW
FCR-D (Power
plant reserves)
1 MW
FCR-D (Relayconnected
loads)
FCR-D (Idle
reserve power
machines)
FRR-A
FRR-M
1 MW
1 MW
5 MW
10 MW
Full activation time
In 3 min after frequency
step change of ± 0,1 Hz
5 s / 50 %
30 s / 100 %, with
frequency 49,50 Hz
Immediately with
frequency 30 s ≤ 49,70 Hz
or 5 s ≤ 49,50 Hz
Reserve should be
activated, when frequency
30 s ≤ 49,70 Hz
2 min
max 15 min
Activation frequency
Other
Constantly
Dead band max ±0,05 Hz,
droop max 6
Several times per day
Load can be reconnected to
Several times per day grid when frequency is at least
49.90 Hz for five mins
Machine can be disconnected
Several times per day from grid when frequency is at
least 49.90 Hz for five minutes
Several times per day
automatic
Several times per day
manual
Right now there is uncertainty and lack of explanation regarding the question how BESS should
be operated in the FCR-D. Additionally, FCR-D requires bigger minimum size, which can be a
challenge for BESS, and offers a significantly smaller payment as shown in
Figure 5.4. FRR-A and FRR-M require even bigger minimum size and operate with long
response time, not utilizing fast response advantage of BESS. Therefore, FCR-N reserve product
has suitable requirements for BESS and will provide bigger payments than FCR-D. The
corresponding simulations will be performed in the next sections.
Figure 5.4. Evolution of frequency containment reserves prices in Finland (Fingrid).
59
5.2 Simulation of BESS at FCR-N
The main goal of the simulations is to observe BESS response to real frequency data, to compare
different energy management strategies and to analyse technical constraints. The energy
management strategies analysis was made from BESS owner point of view, i.e. to minimize
degradation rates and to maximize profits, at the same time fulfilling the TSO requirements.
At the present moment, there is no specific requirements and prequalification rules from Fingrid
for reserve providing units with limited capacity such as BESS. In the majority of EU member
states and in Finland, the maintaining of FCR full power activation is currently required for a
period of 15 minutes. It is assumed that by the end of 15 minutes, the secondary reserves will
be fully activated in order to release the primary reserves. That means that required energy
storage capacity is the key determining cost factor of the BESS, as it will define the maximum
power which can be bidden and the total system investment. The optimal sizing question will
be discussed further in the text. During the comparison of control logics, the minimum
requirement described above will be used.
In this thesis, the capacity and nominal voltage of the BESS was arbitrary chosen to be 1 MWh
and 825 V. The upward (in the case of under frequencies) and downward (in the case of over
frequencies) frequency regulations in Finland are not provided separately. Hence the BESS
should provide regulation in both directions. Considering the normal distribution of frequency
deviation from Figure 5.1, the set point of SoC is assumed to be 50%. However, this is not
always the case, because some storages can be utilized with special control strategies. Most of
the
lithium-ion
battery
manufacturers
highly
recommend
to
operate
it
within
10 – 90 % SoC range, otherwise a rapid battery degradation will take place. Thus, only 40% of
full BESS energy capacity or 0.4 MWh is available to provide 15 minutes’ full power regulation
service as shown in Figure 5.5. Therefore, the maximum FCR-N bidding power of the unit is
defined in Equation 5.1.
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
SoCmax
0.4 MWh
SoCmin
0
3
2
PFCR-N (MW)
100
90
80
70
60
50
40
30
20
10
0
EBESS (MWh)
SoC (%)
60
1
E = 0.4 MWh
0
-1
-2
-3
15
0
Time (min)
15
Time (min)
Figure 5.5. Dimensioning requirement graphical representation.
PFCR  N 
0.4  EBESS 0.4 1 MWh


 1.6 MW
t15min
0.25
h
(5.1)
PFCR  N  FCR-N maximum bidding power [MW]
EBESS
 total BESS capacity [MWh]
t15min
 full activation time period requirement [h]
The number of parallel strings and cells in one string of the BESS needed to parametrize the
model are presented in Equations 5.2 – 5.3.
N par 
EBESS
1
MWh


 484.84  485
VBESS  Ccell 825  2.5 V  Ah
(5.2)
VBESS 825 V

 250
Vcell
3.3 V
(5.3)
N str 
Also, it has to be mentioned that energy capacity of the battery storage will decrease due to
degradation, and maximum bidding power will reduce as well. For example, at 80% state of
health (SoH) of the batteries, the regulation capacity will be 0.32 MWh and the maximum
bidding power will be 1.28 MW.
61
5.2.1 Description of control logics
The first control logic implementation represents the most common understanding of the
frequency dead-band with center at the nominal frequency 50 Hz. Fingrid’s application
instruction for the maintenance of FCR (2016) specifies that “reserve unit used in FCR-N shall
regulate almost linearly within a frequency range of 49.90 - 50.10 Hz so that the dead band in
frequency regulation is at the most 50 ±0.05 Hz.” During the time when the frequency is inside
the dead-band, if SoC is not equal to initial set point level, the controller will initiate charging
or discharging mode to recover the SoC to the reference level. The rate of recovery mode is
equal to ±1 p.u. of the current bidding power PFCR-N, if not stated otherwise. The output power
of the BESS vs. frequency variation of the first control logic is shown in Figure 5.6. The
demonstration of control logic №1 operation during one hour is shown in Figure 5.7.
1,5
Power, p.u
1
0,5
0
49,85
49,9
49,95
50
50,05
50,1
-0,5
-1
-1,5
Frequency, Hz
Figure 5.6. Control logic №1 output power vs. frequency variation, ±0.05 Hz dead-band.
50,15
62
Figure 5.7. Control logic №1 operation (one hour).
European Network of Transmission System Operators for Electricity (ENTSO-E) is discussing
the possibility of tightening the dead-band to ±10 mHz. Without a doubt, it will cause
implications of more frequent activation of BESS and degradation rate increase. However, the
tightening the dead-band can change the market situation or additional payments for BESS can
be introduced. The output power of the BESS vs. frequency variation of the second control logic
is shown in Figure 5.8. The demonstration of control logic №2 operation during one hour is
shown in Figure 5.9.
63
1,5
1
Power, p.u.
0,5
0
49,85
49,9
49,95
50
50,05
50,1
-0,5
-1
-1,5
Frequency, Hz
Figure 5.8. Control logic №2 output power vs. frequency variation, ±0.01 Hz dead-band.
Figure 5.9. Control logic №2 operation (one hour).
50,15
64
Following control logic represent complete absence of dead-band. That case allows evaluating
the contribution of dead-band from degradation rate perspective. The output power of the BESS
vs. frequency variation of the third control logic is shown in Figure 5.10. The demonstration of
control logic №3 operation during one hour is shown in Figure 5.11.
1,5
Power, p.u.
1
0,5
0
49,85
49,9
49,95
50
50,05
-0,5
-1
-1,5
Frequency, Hz
Figure 5.10. Control logic №3 output power vs. frequency variation, no dead-band.
50,1
50,15
65
Figure 5.11. Control logic №3 operation (one hour).
The control logic №4 operates with the common dead-band but with the inclusion of 2 sec
transport delay block. The idea is to react only if the frequency is out of the dead-band for more
than 2 seconds thus ignoring small fluctuations outside the dead-band shorter than 2 sec.
Ignoring very short deviations should reduce degradation rates by a certain amount. Although it
is obviously favorable by BESS owner, each power activation signal will be delayed and cut off
by 2 sec. In fact, it does not violate technical requirements for FCR-N. However, such strategy
reduces advantages from BESS for TSO to some extent. The demonstration of control logic №4
operation with custom frequency signal is shown in Figure 5.12.
66
No activation
> 2 sec
Side effect –
interrupting recovery
Figure 5.12. Control logic №4 operation (30 sec).
The control logic №5 operates with the common dead-band but introduces a new strategy for
recovery mode. There are currently no exact instructions and requirements for how to restore
the energy content of FCR units with limited capacity. Based on the fact that frequency signal
has a normal distribution, it can be suggested that in ideal case SoC will be regulated toward set
point by frequency regulation in opposite direction without additional control. Since the capacity
of storage is limited, the recovery control is still necessary. However, it is more reasonable to
recover faster near the SoC limits than in set point proximity. Consequently, instead of constant
values, recovery power can be described by a function of SoC deviation from the set point. The
hybrid strategy approach described by Li et al. (2014) was selected as a reference and adapted
for the recovery power as shown in Equations 5.4 and 5.5. The difference between regular and
suggested strategy is shown in Figure 5.13. The demonstration of control logic №5 operation
during one hour is shown in Figure 5.14.
67
SoC  SoCref
Prec charge 
(5.4)
SoCmin  SoCref
SoC  SoCref
Prec discharge  
(5.5)
SoCmax  SoCref
Prec charge
 charge power during recovery [p.u.]
Prec discharge
 discharge power during recovery [p.u.]
SoCref
 state of charge setpoint
SoCmin
 state of charge minimum limit
SoCmax
 state of charge maximum limit
1,2
1
0,8
0,6
Power, p.u.
0,4
0,2
0
0
0,1
0,2
0,3
0,4
-0,2
0,5
0,6
0,7
-0,4
-0,6
-0,8
-1
-1,2
State of Charge
Figure 5.13. Control logic №5 recovery power of the BESS vs. SoC deviation.
0,8
0,9
1
68
Figure 5.14. Control logic №5 operation (one hour).
The described control logics were implemented in the form of controller blocks that use
frequency data and SoC as inputs and gives current charge or discharge signal to BESS model.
The layout of developed controller block set in Simulink with control logic №5 can be found in
Appendix VI.
5.2.2 BESS dimensioning and the end of life criterion
The dimensioning of the system is the core question for the overall economic feasibility of the
BESS. Currently, there is an ongoing enactment process of the new ENTSO-E Network Code
(NC) on Load-Frequency Control and Reserves (LFCR) which will introduce specific
requirements for energy constrained units (ENTSO-E 2013). Right now the project is passing
the approval stage, and it is expected that new code will enter into force in 2017.
69
According to the draft version of Commission Regulation (2016) establishing a guideline on
electricity transmission system operation, all TSOs of Continental Europe (CE) and Nordic
synchronous areas shall develop a proposal concerning the minimum activation period to be
ensured by FCR providers with limited energy reservoirs. The period determined shall not be
greater than 30 or smaller than 15 minutes and shall take full account of the results of the cost–
benefit analysis. In the case of frequency deviations that are smaller than a frequency deviation
requiring full FCR activation, an equivalent length of time have to be ensured. An FCR
providers with limited energy reservoirs should also ensure the recovery of the energy reservoirs
in the positive or negative directions at latest within 2 hours after the end of the alert state.
The reason why all TSOs should develop a proposal based on the results of the cost–benefit
analysis, is because there are two points of view. As an explanation for the “30 minutes”
requirement ENTSO-E (2013) claims that it is based on statistical analysis of frequency
deviation patterns and is considered as a compromise between continuous availability and
energy reservoir exhaustion risk. On the other hand, many stakeholders are concerned that the
“30 minutes” requirement will bring negative effects. They suppose that in the first place it will
dramatically increase the cost on the part of FCR provider. Secondly, it could also increase the
cost of FCR procurement and the cost of electricity in the European Union since it will limit the
potential amount of providers.
Another parameter that influences the investment profitability of BESS is the batteries EoL
principle. First of all, there is no determined or prescribed criterion for each application. Usually,
the value of 80% is used, which means that battery lost 20% of initial nominal capacity.
However, in practice, the effective EoL capacity value might differ from commonly acceptable.
For example, operating the BESS until 60% of capacity will limit the maximum bidding power
as time goes by and reduce the income, but the time period between the investments in new
batteries will increase.
70
In conclusion, the simulations were performed for a range of capacity time period requirements
namely 15, 20, 25 and 30 minutes, with EoL of 80%, 70% and 60% in each examined case. The
utilized control logic is justified after comparison in section 5.4.1.
5.3 Methodology
In this section, the methodology used to compare different BESS control strategies and other
parameters based on the lifetime estimation and investment profitability is explained.
5.3.1 Lifetime estimation
The model itself does not predict the lifetime of the system; it can only calculate degradation
amount during the simulation and set initial SoH. The simulation of several years’ time is not
an adequate way to get lifetime value because it will take too much time and memory. One
month was assumed to be a sufficiently representative period of time. Therefore, the lifetime of
the BESS was estimated by fitting the total capacity loss curve with power function and
extrapolating it. The example of lifetime estimation process for control logic №1 is presented in
Figure 5.15.
Figure 5.15. BESS lifetime estimation process (Qnom=2.5 Ah, consequently 20% = 0.5 Ah, 40% = 1 Ah).
71
5.3.2 Assessment of net present value
Economic feasibility of an investment can be estimated by calculating net present value (NPV)
as shown in Equation 5.6.
n
NPV  
i 1
NPV
 net present value [EUR]
Ct
 cash flow [EUR]
C0
 initial investment [EUR]
r
 discount rate
t
 number of cash flow year
n
 number of years for analysis
Ct
 C0
(1  r )t
(5.6)
In actuality, the installed costs of BESS comprises several components. Besides the batteries,
the system must include power conditioning and transformation equipment, interfaces and
controls, physical housing, cooling system and other necessary equipment. In addition, the
project engineering, installation, operations and maintenance costs should be considered too.
Therefore, the reported costs of energy storage are only estimates. GTM Research (2016) reports
at year-end 2015 a system price of large-scale lithium-ion BESS within an estimated range of
700 - 1200 $/kWh. For the following NPV assessment, the installation price of 900 EUR/kWh
were assumed.
Annual income is based on a yearly agreement with Fingrid for providing FCR-N service. The
capacity fee in 2016 is 17.42 €/MW,h and assumed to be the same for the following years. The
reserve plans are made for 24 h every day, so total annual time is 8760 h. The fines for
unavailability are calculated in accordance with Fingrid (2016) rules: “Reserve Holder shall pay
Fingrid 50 per cent of the above price, in other words, 8.71 €/MW,h, in compensation for
capacity not supplied.” As mentioned before, the remaining capacity of the BESS is gradually
fading, and so the maximum bidding power is reducing. Since the agreement is concluded at the
72
beginning of the year, to ensure its’ obligations at the end of the year the FCR-N provider should
make a contract for volume expected by the end of the year.
The investment profitability was calculated for a period of estimated lifetime with a discount
rate of 5%. The example of cash flows and NPV assessment for 1.6 MW / 1 MWh BESS with
60% EOL criterion and control logic №1 employed is shown in Table 5.2 and Figure 5.16.
Table 5.2. BESS cash flows and NPV calculation.
0
1.00
Max
bidding
power,
MW
1.60
1
0.89
1.43
0
215 202
-1 592
213 611
95%
203 439
-696 561
2
0.85
1.35
0
203 623
-1 506
202 117
91%
183 326
-513 235
3
0.81
1.29
0
194 542
-1 439
193 103
86%
166 810
-346 425
4
0.78
1.24
0
186 779
-1 381
185 398
82%
152 527
-193 898
5
0.75
1.20
0
179 869
-1 330
178 539
78%
139 890
-54 008
6
0.72
1.15
0
173 571
-1 284
172 287
75%
128 563
74 556
7
0.70
1.12
0
167 739
-1 241
166 499
71%
118 328
192 883
8
0.67
1.08
0
162 280
-1 200
161 079
68%
109 025
301 908
9
0.65
1.04
0
157 126
-1 162
155 964
64%
100 535
402 444
10
0.63
1.01
0
152 229
-1 126
151 103
61%
92 764
495 208
11
0.61
0.98
0
147 552
-1 091
146 461
58%
85 633
580 840
11.7
0.60
0.96
0
101 076
-748
100 328
57%
56 690
637 530
Remained
Year capacity,
MWh
Installed
costs,
EUR
Income,
EUR
Penalty
costs,
EUR
-900 000
0
0
Present
Present
value of Cumulative
value
cash flow, NPV, EUR
factor
EUR
-900 000 100%
-900 000
-900 000
Cash
flow,
EUR
The total amount of energy throughput is 2597.72 MWh, and price of electricity is 40
EUR/MWh with battery efficiency 95%, then possible losses can be estimated in Equation 5.7.
The value of losses is too small compared to NPV, so it can be neglected.
Closs  VBESS  Ahth  сloss     3148755  40 106  0.05  5195.5 EUR
Ce
 loss due to efficiency [EUR]
ce
 electricity price [EUR/MWh]

 battery efficiency [%]
(5.7)
73
800 000
Cumulative NPV, EUR
600 000
400 000
200 000
0
-200 000
0
1
2
3
4
5
6
7
8
9
10
11
12
-400 000
-600 000
-800 000
-1 000 000
Year
Present value of cash flow, EUR
Cumulative NPV, EUR
Figure 5.16. BESS present values graph.
5.4 Simulation results
Five control logics described above were simulated using the real frequency data profile of
March 2016 measured at 400 kV substations at different locations in Finland, with 1 second
sample time. The rated power and energy capacity of the BESS was set to
1.6 MW and 1 MWh consequently. The ambient temperature of the batteries assumed to be
20°C.
5.4.1 Comparison of control logics
Figure 5.17 shows the resulting SoC graphs of the BESS during simulations, and Figure 5.18
shows the evolution of cell capacity loss curves for different control logics.
The strategies worked as expected except №2 and №3. The capacity loss of strategy without a
dead-band is smaller than with a ±0.01 Hz dead-band. That can be explained due to the longer
idling periods in control strategy №3 and can be seen on the SoC graphs. Notwithstanding the
degradation rates, control logics №2 and №3 activate the BESS too often and therefore have
problems with the frequent reaching of the SoC limits which calls into question the applicability
74
of such strategies. It means that reduction of the dead-band will have a huge effect on BESS
sizing and overall profitability unless the compensation payments will be introduced.
Figure 5.17. SoC simulation results for different control logics (one month period).
75
Figure 5.18. Cell capacity loss simulation results for different control logics.
The lifetime until 80% SoH and corresponding NPV of BESS are presented in Table 5.3.
Table 5.3. Results and comparison of the control logics.
Control logic
Lifetime, years
SoC saturation idling time per month, h
Net present value, EUR
№1
3.244
10.64
-306 617
№2
2.446
132.82
-563 533
№3
3.562
254.11
-583 298
№4
3.25
10.73
-305 692
№5
3.37
12.97
-287 488
The suggested 2 seconds “ignoring-delay” approach in control strategy №4 provided only
925 EUR gain of NPV. Such a slight difference cannot be considered as a clear improvement
and therefore it will not be utilized in further simulations.
Control logic №1 fulfills its function without a problem, but simplified recovery strategy leads
to shorter lifetime compared to smooth recovery in control logics №5. The cause of larger
degradation in logic №1 is because SoC level recovers too fast even if the deviation is not so
huge. Although slower recovery increases the risk of BESS exhaustion and leads to longer SoC
76
saturation idling time, the benefits from prolonged lifetime is more valuable for the BESS owner
than the cost of unavailability fines.
In conclusion, the control logic №5 have shown the highest NPV in the analysis among other
candidates and hence it will be employed in the further analysis.
5.4.2 Sensitivity analysis
The requirement obligating FCR providing a unit to activate full capacity for a specific period
of time is basically a way to limit the power-to-energy ratio (MW/MWh rating). For following
cases, the energy capacity of the BESS assumed to stays the same as 1 MWh. By substituting
the different time period in Equation 5.1, the maximum bidding powers of 15, 20, 25 and 30
minutes’ requirements are 1.6 MW, 1.2 MW, 0.96 MW and 0.8 MW, consequently.
The simulations were performed using control logic №5 and EoL range 50-80%.
Results are presented in Table 5.4. NPV and cash flows calculations for the most representative
cases can be found in Appendix VII.
Table 5.4. Lifetime and cost-benefit estimation of simulated cases.
Full activation
Maximum bidding SoC saturation idling
time period
power, MW
time per month, h
requirement, min
12.97
13.05
15
1.6
13.09
13.14
7.69
7.73
20
1.2
7.75
7.80
4.62
4.64
25
0.96
4.67
4.72
3.05
3.06
30
0.8
3.09
3.13
EoL, %
Lifetime, years
Net present
value, EUR
80
70
60
50
80
70
60
50
80
70
60
50
80
70
60
50
3.37
7.12
12.13
18.28
4.11
8.65
14.67
22.08
4.73
9.90
16.73
25.07
5.32
11.09
18.67
27.91
-287 488
207 324
673 281
1 043 467
-340 634
92 736
479 251
770 554
-385 814
-3 657
318 585
552 587
-423 374
-83 497
198 069
391 671
77
To have a better visual understanding of the dependencies, the surface plot of NPV with two
variables is presented in Figure 5.19.
Figure 5.19. NPV surface plot with power-to-energy and EoL variables.
Firstly, there is a clear pattern of how EoL criterion is affecting the NPV of the BESS project.
The dependency is non-linear, with more NPV for lower EoL principle. Indeed, the specific of
frequency regulation unit is that it can make new contracts every year for the smaller amount of
reserve power. However, in real life BESS cannot be employed until it will lose all 100% of the
capacity. Naumann et al. (2015) explain that at a certain point of a lifetime, new nonlinear aging
mechanisms can be revealed. The results would be a strong decrease of capacity and a strong
increase of internal resistance, i.e. decrease of battery efficiency. That phenomenon greatly
depends on cell chemistries and prior use conditions. Currently, there is no adequate
78
understanding of how the second-life batteries (SoH < 80%) should be operated correctly. Now
it is one of the questions, which has drawn the attention of the scientific community because
using second-life batteries in unassuming applications can significantly reduce the costs. In the
meantime, this thesis assumes that operating batteries under 60% of nominal capacity are not
possible.
Secondly, the investment profitability is decreasing with the lower power-to-energy ratio, i.e.
raising the level of full power active time requirement will negatively affect the value of energy
storages on FCR markets. Nevertheless, the model demonstrated a positive NPV for a quite big
area of cases. Figure 5.20 shows how the surface plot results from Figure 5.19 represented in
the way so it can be seen what combination of variables will produce positive NPV. It goes
without saying that economics of the system depends on many other factors and the transition
between “profitable” and “not profitable” should rather be perceived as smooth.
Figure 5.20. Gradient area of the positive NPV estimation.
79
As it was mentioned in Section 5.2.2, many stakeholders have an opinion that the doubling of
full activation time requirement will severely decrease the profitability of limited energy
storages. Whereas the results of the conducted simulations show that NPV of cases with
80% EoL, which is probably the most common approach, have a quite small impact from powerto-energy ratio change. On the other hand, the influence of EoL criterion on NPV is rather big.
At last, the price of the lithium-ion batteries has a direct impact on the NPV. Many academic
sources in the past claimed economic unreasonableness due to high prices. After a long price
development process, it seems that prices reached the level when it can bring profits with certain
assumptions. Figure 5.21 and 5.22 show the relationship between system installed costs and
NPV of BESS ranging from 15 min to 30 min requirements duration for 80% and 60% EoL
criterion respectively.
Figure 5.21. NPV sensitivity analysis with the variable system installed price (80% EoL).
80
Figure 5.22. NPV sensitivity analysis with the variable system installed price (60% EoL).
It can be observed that, based on developed model and all other considerations with common
80% EoL approach, it would require further price reduction approximately in half. While the
60% EoL criterion is theoretically justifying the BESS with the current price values.
81
6 CONCLUSION
The presented study has investigated technical and economic aspects of lithium-ion BESS in
grid-scale applications from the point of view of BESS owner (operator). In general terms, it
required a comprehensive analysis of literature, employment, and development of the models,
as well as relevant methodologies.
Lithium-ion technologies are considered as viable solutions for many high power or high energy
applications and represent a broad family of chemistries each with their own features and
properties. This thesis particularly justified and considered LFP cells type in conjunction with
selected application. One of the main challenges of working with electrochemical cells is the
appropriate lifetime estimation and understanding the phenomena behind the aging processes.
It becomes essentially vital in order to form a link from operating conditions to lifetime and
eventually the economic feasibility of a BESS. This thesis provided the literature review with
necessary up-to-date background information about lithium-ion cells, including the main
features, development progress, and aging mechanisms. An adequate LFP cell lifetime model
was selected as a result of the publically available models comparison.
On the next stage, the study developed a practical lithium-ion BESS model with the ability to
describe dynamic performance behavior and to estimate degradation effects. The model was
implemented in Matlab/Simulink modeling environment. It was found to perform its functions
accurately and effectively. To demonstrate the use of the developed model, it was employed for
simulation of primary frequency regulation provided by BESS.
The feasibility assessment of providing the frequency regulation using BESS in Finland was
selected as a study case. The relevance and demand of such a service in Nordic countries were
emphasized. To perform a BESS control management based on frequency input data, five
different control logics were implemented and described in details. The control logics
comparison found the strategy proposed in this thesis to have advantages over the traditional
fixed droop. The questions related to the application such as BESS dimensioning, EoL criterion,
82
overall system costs, lifetime estimation and economic assessment were discussed. Results from
the techno-economic analysis revealed profitable and implementable system cases.
6.1 Future work
There are many possibilities for further improvement and to continue the presented research.
One of the improvements can refer to developing more advanced lifetime model, which will
consider more stress factors or increase the overall estimation accuracy. Regarding the
equivalent circuit-based model, the coulumbic counting SoC estimation method can be
improved by more advanced methods. The resistance increase and efficiency of the battery can
be also taken into account.
The control strategies for BESS operated at frequency regulation can be improved, or optimized
or even invented the novel approaches. The more advanced and accurate economic evaluation
methods can be utilized. Other state markets can be investigated as well. The BESS benefits
increase by combining different provided services and how it influence on the service quality
and requirements is very interesting and relevant topic. Also mentioned in the text, the potential
of utilizing second-life batteries could bring significant costs decrease, but it needs to be also
investigated from the technical point of view.
It would be interesting to investigate the case feasibility of BESS providing frequency regulation
at conventional power plants. For example in Russia, all power plants have to participate in
frequency regulation, except some nuclear plants. Participating in frequency regulation means
certain units are not working with optimal efficiency, therefore losing possible profits. Instead,
power plants could meet the regulation commitments with the help of BESS while operating the
generator units with optimal cost-efficient level.
83
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Appendix I, 1
Appendix I. Battery cell terminology
Cell capacity
Nominal capacity (Qnom ) represents capacity labeled on cell specification by the manufacturer.
Remaining capacity (Qr ) represents the accessible capacity of the cell. The remaining capacity
of the new cell should be equal to nominal capacity. Faded capacity (Qloss ) represents capacity
lost due to degradation.
State of health (SoH)
The term state of health (SoH) is used to describe the state of the cell between the beginning of
life (BoL) and end of life (EoL). The value of 100% means the cell with full nominal capacity
and value of 0% means the cell without the ability to store any energy.
State of charge (SoC)
The state of charge (SoC) indicates a percentage of active charge stored in the cell at certain
moment of time
Cycle
In general, the cycle is described as a sequence of a discharge followed by a charge or vice
versa. Full cycle indicates a complete discharging and charging event with 100% DoD (i.e.
emptying and refilling the whole capacity). The term equivalent full cycle is defined by the
amount of energy processed through the battery with any DoD swing divided by the nominal
capacity.
Current rate (C-rate)
The C-rate is the current scaled to the nominal capacity of a cell stated by the manufacturer
(MIT Electric Vehicle Team 2008, 1). A current discharge rate of 1C means that battery cell
Appendix I, 2
will be discharged from SoC = 100% to SoC = 0% in 1 hour. For example, for a cell with a
nominal capacity of 100 Ah, 1C current will be 100 A.
Open-Circuit Voltage (OCV)
The OCV of the cell is defined as the voltage between terminals in the state of electrochemical
equilibrium with no load applied. The OCV strongly depends on the SoC at any moment of
time.
Appendix II, 1
Appendix II. Lithium-ion cell used in model development
Appendix III, 1
Capacity fade, %
Appendix III. Calendar degradation models additional data
8
7
6
5
4
3
2
1
0
Yuckel and Michalek (2012)
Grolleau et al. (2014)
Sqierczynsky et al. (2015a)
Swierczynski et al. (2015b)
Kassem et al. (2012)
reconstructed
0
100
200
300
t, days
400
500
600
Mean value;
Capacity fade, %
Figure C.1. Calendar degradation data acquired from examined models and sources (T=30°C, 50% SoC).
20
Yuckel and Michalek (2012)
15
Grolleau et al. (2014)
10
Sqierczynsky et al. (2015a)
Kassem et al. (2012)
reconstructed
5
Li et al. (2016) reconstructed
0
0
100
200
300
t, days
400
500
600
Swierczynski et al. 2015b
Figure C.2. Calendar degradation data acquired from examined models and sources (T=45°C, 50% SoC).
Capacity fade, %
50
Yuckel and Michalek (2012)
40
Grolleau et al. (2014)
30
Sqierczynsky et al. (2015a)
20
Swierczynski et al. (2015b)
10
Kassem et al. (2012)
reconstructed
0
0
100
200
300
t, days
400
500
600
Le et al. (2016) reconstructed
Figure C.3. Calendar degradation data acquired from examined models and sources (T=60°C, 50% SoC).
Appendix IV, 1
Appendix IV. Model initialization file
%
%
%
%
%
Initialization file for ssc_lithium_cell_2RC_BESS
Parameters of A123 system’s ANR26650 LiFePO4/graphite cell
Copyright 2012 The MathWorks, Inc.
With upgrades from Ignatev Eduard ([email protected])
%% BESS size
% Number of parallel strings
N_par = 485; % 485 for 1212.5 Ah (1000 kWh) total capacity
% Number of cells in one string
N_str = 250; % 250 for 825 V nominal voltage
% FCR-N bidding power
P_fcr = 1.6e6; % W
%% Initial Conditions
% State of Health
SOH = 1; %0..1
% Charge deficit
Qe_init = 1.25; %Ampere*hours
% Ambient Temperature
T_init = 20 + 273.15; %K
%% Lookup Table Breakpoints
SOC_LUT = [0 0.025 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.975 1]';
Temperature_LUT = [15 25 35 45] + 273.15;
%% Em Branch Properties (OCV, Capacity)
% Nominal battery capacity
Capacity_nom = [
2.50 2.50 2.50 2.50]; %Ampere*hours
Capacity_LUT = Capacity_nom .* SOH; %Ampere*hours
% Em open-circuit
Em_LUT = [
2.730 2.730
2.933 2.933
3.079 3.079
3.204 3.204
3.250 3.250
3.283 3.283
voltage vs SOC rows and T columns
2.730
2.933
3.079
3.204
3.250
3.283
2.730
2.933
3.079
3.204
3.250
3.283
Appendix IV, 2
3.300
3.306
3.309
3.322
3.346
3.351
3.369
3.414
3.532
]; %Volts
3.300
3.306
3.309
3.322
3.346
3.351
3.369
3.414
3.532
3.300
3.306
3.309
3.322
3.346
3.351
3.369
3.414
3.532
3.300
3.306
3.309
3.322
3.346
3.351
3.369
3.414
3.532
%% Terminal Resistance Properties
% R0 resistance vs SOC rows
R0_LUT = [
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
0.0134 0.0104 0.0090
]; %Ohms
and T columns
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
%% RC Branch 1 Properties
% R1 Resistance vs SOC rows
R1_LUT = [
0.0296 0.0181 0.0135
0.0296 0.0181 0.0135
0.0290 0.0180 0.0134
0.0279 0.0178 0.0131
0.0255 0.0172 0.0125
0.0233 0.0160 0.0115
0.0240 0.0179 0.0134
0.0233 0.0169 0.0122
0.0200 0.0141 0.0103
0.0184 0.0128 0.0100
0.0188 0.0146 0.0125
0.0204 0.0150 0.0114
0.0216 0.0151 0.0111
0.0223 0.0151 0.0110
0.0223 0.0151 0.0110
]; %Ohms
and T columns
0.0111
0.0111
0.0109
0.0107
0.0097
0.0092
0.0100
0.0095
0.0082
0.0082
0.0103
0.0089
0.0086
0.0085
0.0085
Appendix IV, 3
% C1 Capacitance vs SOC rows and T columns
C1_LUT = [
1076
1758
2616
3155
1132
1796
2560
3080
1182
1834
2522
3023
1308
1877
2447
2911
1527
1877
2241
2641
1852
2172
2485
2710
2078
2447
2760
2923
2021
2253
2447
2579
2003
2322
2648
2961
2228
2673
3286
3474
2479
3267
3668
3743
2479
2804
2817
2873
2479
2629
2648
2729
2479
2566
2591
2685
2479
2510
2560
2654
]; %Farads
% R2 Resistance vs SOC rows
R2_LUT = [
0.1260 0.1079 0.0946
0.1133 0.0877 0.0830
0.1024 0.0774 0.0728
0.0752 0.0596 0.0503
0.0284 0.0221 0.0176
0.0247 0.0186 0.0133
0.0354 0.0212 0.0115
0.0240 0.0156 0.0106
0.0207 0.0141 0.0095
0.0422 0.0220 0.0181
0.0433 0.0258 0.0157
0.0245 0.0149 0.0099
0.0164 0.0099 0.0079
0.0112 0.0080 0.0072
0.0058 0.0064 0.0066
]; %Ohms
and T columns
0.0830
0.0728
0.0628
0.0510
0.0167
0.0114
0.0086
0.0079
0.0076
0.0112
0.0107
0.0069
0.0059
0.0058
0.0058
% C2 Capacitance vs SOC rows and T columns
C2_LUT = [
270
540
809
1619
8633
11331
12140
12410
16727
21313
22662
22122
31025
38040
39658
34532
49101
65018
83633
98471
45594
72572
99550 119245
29946
41547
75000 132734
48022
70414 102788 133004
61781
84982 121133 141097
36421
46403
47482
59353
27248
35881
55036
76079
40737
65288
89838 114119
Appendix IV, 4
47482
82824
52068
91996
60701 102518
]; %Farads
109802
123291
144604
135162
146493
159442
%% Thermal Properties
% Cell dimensions and sizes
%cell_thickness = 0.0084; %m
cell_width = 0.026; %m
cell_height = 0.065; %m
cell_radius = 0.013; %m
% Cell surface area
% cell_area = 2 * (...
%
cell_thickness * cell_width +...
%
cell_thickness * cell_height +...
%
cell_width * cell_height); %m^2
cell_area = 2 * 3.14 * cell_height * cell_radius; %m^2
% Cell volume
cell_volume = 3.14 * cell_height * cell_radius^2; %m^3
% Cell mass
cell_mass = 0.076; %kg
% Volumetric heat capacity
% assumes uniform heat capacity throughout the cell
% ref: J. Electrochemical Society 158 (8) A955-A969 (2011) pA962
cell_rho_Cp = 2.04E6; %J/m3/K
% Specific Heat
cell_Cp_heat = cell_rho_Cp * cell_volume; %J/kg/K
% Convective heat transfer coefficient
% For natural convection this number should be in the range of 5 to 25
h_conv = 20; %W/m^2/K
Appendix V, 1
Appendix V. Degradation functions contents
function Q_cyc = fcn(Ah_th, T, Capacity_nom)
%#codegen
%Initial capacity [Ampere*hours]
Cap_init = Capacity_nom(2);
%Calendar degradation function [Ampere*hours]
Q_cyc = 0.00024 * exp(0.02717 * (T + 273.15)) * 0.02982 ...
* sqrt(abs(Ah_th) * 100 / (3600 * 2 * Cap_init)) *
Cap_init/100;
function Q_cal = fcn(t, T, SOC, Capacity_nom)
%#codegen
%Initial capacity [Ampere*hours]
Cap_init = Capacity_nom(2);
%Calendar degradation function [Ampere*hours]
Q_cal = (0.019 * (abs(SOC) * 100)^0.823 + 0.5195) ...
* (3.258 * 10^(-9) * abs(T)^5.087 + 0.295) ...
* (t * 3.8 * 10^(-7))^0.8 * Cap_init/100;
Appendix VI, 1
Appendix VI. Controller Simulink block set of control logic №5
Appendix VII, 1
Appendix VII. Representative cases NPV calculation
Table VII.1. BESS cash flows and NPV calculation (1.6 MW/1 MWh; EoL - 60% SoH; control logic №5).
Max
Remained
bidding
Year capacity,
power,
MWh
MW
1.00
1.60
0
0.90
1.43
1
0.85
1.36
2
0.81
1.30
3
0.78
1.25
4
0.75
1.20
5
0.73
1.16
6
0.70
1.12
7
0.68
1.09
8
0.66
1.06
9
0.64
1.02
10
0.62
0.99
11
0.60
0.96
12
0.60
0.96
12.13
Installed
costs,
EUR
Income,
EUR
Penalty
costs,
EUR
-900 000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
215 033
203 711
194 828
187 233
180 470
174 305
168 596
163 251
158 204
153 409
148 829
144 436
18 704
0
-1 945
-1 842
-1 762
-1 693
-1 632
-1 576
-1 525
-1 476
-1 431
-1 387
-1 346
-1 306
-169
Present
Present
value of Cumulative
value
cash flow, NPV, EUR
factor
EUR
-900 000 100%
-900 000
-900 000
213 088
95%
202 941
-697 059
201 868
91%
183 101
-513 958
193 066
86%
166 778
-347 181
185 539
82%
152 644
-194 537
178 838
78%
140 124
-54 413
172 729
75%
128 893
74 480
167 071
71%
118 735
193 215
161 774
68%
109 495
302 710
156 773
64%
101 058
403 767
152 021
61%
93 328
497 095
147 483
58%
86 230
583 326
143 130
56%
79 700
663 026
18 535
55%
10 256
673 281
Cash
flow,
EUR
Table VII.2. BESS cash flows and NPV calculation (1.6 MW/1 MWh; EoL - 80% SoH; control logic №5).
Year
0
1
2
3
3.37
Max
Remained
bidding
capacity,
power,
MWh
MW
1.00
1.60
0.90
1.43
0.85
1.36
0.81
1.30
0.80
1.28
Installed
costs,
EUR
Income,
EUR
Penalty
costs,
EUR
-200 000
0
0
0
0
0
215 033
203 711
194 828
71 003
0
-1 945
-1 842
-1 762
-642
Present
Present
value of Cumulative
value
cash flow, NPV, EUR
factor
EUR
-200 000 100%
-200 000
-200 000
213 088
95%
202 941
2 941
201 868
91%
183 101
186 042
193 066
86%
166 778
352 819
70 361
85%
59 693
412 512
Cash
flow,
EUR
Appendix VII, 2
Table VII.3. BESS cash flows and NPV calculation (0.8 MW/1 MWh; EoL - 60% SoH; control logic №5).
Max
Remained
bidding
Year capacity,
power,
MWh
MW
1.00
0.80
0
0.92
0.74
1
0.88
0.71
2
0.85
0.68
3
0.83
0.66
4
0.81
0.65
5
0.79
0.63
6
0.77
0.61
7
0.75
0.60
8
0.73
0.59
9
0.72
0.57
10
0.70
0.56
11
0.69
0.55
12
0.67
0.54
13
0.66
0.53
14
0.65
0.52
15
0.63
0.51
16
0.62
0.50
17
0.61
0.49
18
0.60
0.48
18.67
Installed
costs,
EUR
Income,
EUR
Penalty
costs,
EUR
-900 000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
111 942
107 436
103 880
100 829
98 105
95 616
93 307
91 141
89 094
87 147
85 285
83 498
81 776
80 112
78 501
76 938
75 417
73 936
48 886
0
-235
-225
-218
-212
-206
-201
-196
-191
-187
-183
-179
-175
-172
-168
-165
-161
-158
-155
-103
Present
Present
value of Cumulative
value
cash flow, NPV, EUR
factor
EUR
-900 000 100%
-900 000
-900 000
111 707
95%
106 388
-793 612
107 210
91%
97 243
-696 369
103 662
86%
89 547
-606 822
100 617
82%
82 778
-524 044
97 899
78%
76 706
-447 338
95 415
75%
71 200
-376 137
93 111
71%
66 172
-309 965
90 950
68%
61 559
-248 407
88 908
64%
57 311
-191 096
86 964
61%
53 389
-137 707
85 106
58%
49 760
-87 947
83 323
56%
46 397
-41 550
81 604
53%
43 277
1 726
79 944
51%
40 377
42 103
78 337
48%
37 681
79 785
76 776
46%
35 172
114 957
75 259
44%
32 835
147 792
73 781
42%
30 658
178 450
48 784
40%
19 619
198 069
Cash
flow,
EUR
Table VII.4. BESS cash flows and NPV calculation (0.8 MW/1 MWh; EoL - 80% SoH; control logic №5).
Year
0
1
2
3
4
5
5.32
Max
Remained
bidding
capacity,
power,
MWh
MW
1.00
0.80
0.92
0.74
0.88
0.71
0.85
0.68
0.83
0.66
0.81
0.65
0.80
0.64
Installed
costs,
EUR
Income,
EUR
Penalty
costs,
EUR
-900 000
0
0
0
0
0
0
0
111 942
107 436
103 880
100 829
98 105
31 131
0
-235
-225
-218
-212
-206
-65
Present
Present
value of Cumulative
value
cash flow, NPV, EUR
factor
EUR
-900 000 100%
-900 000
-900 000
111 707
95%
106 388
-793 612
107 210
91%
97 243
-696 369
103 662
86%
89 547
-606 822
100 617
82%
82 778
-524 044
97 899
78%
76 706
-447 338
31 066
77%
23 964
-423 374
Cash
flow,
EUR